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This paper is the third in a series of four papers aiming to describe the (almost integral) Chow ring of M¯3, the moduli stack of stable curves of genus 3. In this paper, we compute the Chow ring of M~37 with Z[1/6]-coefficients., QC 20240926

In this paper, we demonstrate the significance of restoring harmonics of the fundamental frequency (pitch) in the deep neural network (DNN)-based speech enhancement. The parameters of the DNN can be estimated by minimizing the mask loss, but it does not restore the pitch harmonics, especially at higher frequencies. In this paper, we propose to restore the pitch harmonics in the spectral domain by minimizing cepstral loss around the pitch peak. Restoring the cepstral pitch peak, in turn, helps in restoring the pitch harmonics in the enhanced spectrum. The proposed cepstral pitch-peak loss acts as an adaptive comb filter on voiced segments and emphasizes the pitch harmonics in the speech spectrum. The network parameters are estimated using a combination of mask loss and cepstral pitch-peak loss. We show that this combination offers the complementary advantages of enhancing both the voiced and unvoiced regions. The DNN-based methods primarily rely on the network architecture, and hence, the prediction accuracy improves with the increasing complexity of the architecture. The lower complex models are essential for real-time processing systems. In this work, we propose a compact model using a sliding-window attention network (SWAN). The SWAN is trained to regress the spectral magnitude mask (SMM) from the noisy speech signal. Our experimental results demonstrate that the proposed approach achieves comparable performance with the state-of-the-art noncausal and causal speech enhancement methods with much lesser computational complexity. Our three-layered noncausal SWAN achieves 2.99 PESQ on the Valentini database with only 10 9 floating-point operations (FLOPs).

In this paper, we demonstrate the significance of restoring harmonics of the fundamental frequency (pitch) in the deep neural network (DNN)-based speech enhancement. The parameters of the DNN can be estimated by minimizing the mask loss, but it does not restore the pitch harmonics, especially at higher frequencies. In this paper, we propose to restore the pitch harmonics in the spectral domain by minimizing cepstral loss around the pitch peak. Restoring the cepstral pitch peak, in turn, helps in restoring the pitch harmonics in the enhanced spectrum. The proposed cepstral pitch-peak loss acts as an adaptive comb filter on voiced segments and emphasizes the pitch harmonics in the speech spectrum. The network parameters are estimated using a combination of mask loss and cepstral pitch-peak loss. We show that this combination offers the complementary advantages of enhancing both the voiced and unvoiced regions. The DNN-based methods primarily rely on the network architecture, and hence, the prediction accuracy improves with the increasing complexity of the architecture. The lower complex models are essential for real-time processing systems. In this work, we propose a compact model using a sliding-window attention network (SWAN). The SWAN is trained to regress the spectral magnitude mask (SMM) from the noisy speech signal. Our experimental results demonstrate that the proposed approach achieves comparable performance with the state-of-the-art noncausal and causal speech enhancement methods with much lesser computational complexity. Our three-layered noncausal SWAN achieves 2.99 PESQ on the Valentini database with only 10 9 floating-point operations (FLOPs).

In this paper the authors propose a new approach to the study of weight systems. Instead of considering graphs whose vertices correspond to the generators of a Lie algebra (as for Cartan subalgebras in the semisimple case), the authors consider the whole weight system. The purpose is to extract information about the weight system from the geometry of the weights. The considerations are restricted to the case where a torus of derivations induces a decomposition of a nilpotent Lie algebra g into one-dimensional weight spaces, none of which is associated with the zero weight. The paper is structured as follows: In Section 2 the most important facts of weight systems of nilpotent Lie algebras and the root system associated to solvable Lie algebras are recalled. In Section 3 the authors formulate their conditions on the weight systems and analyze the consequences of these conditions on the structure of the weight system. They also define associated weight graphs and deduce their elementary geometrical properties. This provides a characterization of the three-dimensional Heisenberg Lie algebra in terms of trees. Section 4 is devoted to the study of certain subgraphs of a weight graph which can be used to reconstruct the weight system from the weight graph. If r is a semidirect product of g and a torus T these subgraphs determine bounds for the solvability class of r . In Section 5 these results are applied to obtain a geometrical proof of the nonexistence of two-step solvable rigid Lie algebras., Depto. de Álgebra, Geometría y Topología, Fac. de Ciencias Matemáticas, TRUE, pub

In this paper, we demonstrate the significance of restoring harmonics of the fundamental frequency (pitch) in the deep neural network (DNN)-based speech enhancement. The parameters of the DNN can be estimated by minimizing the mask loss, but it does not restore the pitch harmonics, especially at higher frequencies. In this paper, we propose to restore the pitch harmonics in the spectral domain by minimizing cepstral loss around the pitch peak. Restoring the cepstral pitch peak, in turn, helps in restoring the pitch harmonics in the enhanced spectrum. The proposed cepstral pitch-peak loss acts as an adaptive comb filter on voiced segments and emphasizes the pitch harmonics in the speech spectrum. The network parameters are estimated using a combination of mask loss and cepstral pitch-peak loss. We show that this combination offers the complementary advantages of enhancing both the voiced and unvoiced regions. The DNN-based methods primarily rely on the network architecture, and hence, the prediction accuracy improves with the increasing complexity of the architecture. The lower complex models are essential for real-time processing systems. In this work, we propose a compact model using a sliding-window attention network (SWAN). The SWAN is trained to regress the spectral magnitude mask (SMM) from the noisy speech signal. Our experimental results demonstrate that the proposed approach achieves comparable performance with the state-of-the-art noncausal and causal speech enhancement methods with much lesser computational complexity. Our three-layered noncausal SWAN achieves 2.99 PESQ on the Valentini database with only 10 9 floating-point operations (FLOPs). © 2022, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.

In this paper, we demonstrate the significance of restoring harmonics of the fundamental frequency (pitch) in the deep neural network (DNN)-based speech enhancement. The parameters of the DNN can be estimated by minimizing the mask loss, but it does not restore the pitch harmonics, especially at higher frequencies. In this paper, we propose to restore the pitch harmonics in the spectral domain by minimizing cepstral loss around the pitch peak. Restoring the cepstral pitch peak, in turn, helps in restoring the pitch harmonics in the enhanced spectrum. The proposed cepstral pitch-peak loss acts as an adaptive comb filter on voiced segments and emphasizes the pitch harmonics in the speech spectrum. The network parameters are estimated using a combination of mask loss and cepstral pitch-peak loss. We show that this combination offers the complementary advantages of enhancing both the voiced and unvoiced regions. The DNN-based methods primarily rely on the network architecture, and hence, the prediction accuracy improves with the increasing complexity of the architecture. The lower complex models are essential for real-time processing systems. In this work, we propose a compact model using a sliding-window attention network (SWAN). The SWAN is trained to regress the spectral magnitude mask (SMM) from the noisy speech signal. Our experimental results demonstrate that the proposed approach achieves comparable performance with the state-of-the-art noncausal and causal speech enhancement methods with much lesser computational complexity. Our three-layered noncausal SWAN achieves 2.99 PESQ on the Valentini database with only 10 9 floating-point operations (FLOPs). © 2022, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.

In this paper, we demonstrate the significance of restoring harmonics of the fundamental frequency (pitch) in the deep neural network (DNN)-based speech enhancement. The parameters of the DNN can be estimated by minimizing the mask loss, but it does not restore the pitch harmonics, especially at higher frequencies. In this paper, we propose to restore the pitch harmonics in the spectral domain by minimizing cepstral loss around the pitch peak. Restoring the cepstral pitch peak, in turn, helps in restoring the pitch harmonics in the enhanced spectrum. The proposed cepstral pitch-peak loss acts as an adaptive comb filter on voiced segments and emphasizes the pitch harmonics in the speech spectrum. The network parameters are estimated using a combination of mask loss and cepstral pitch-peak loss. We show that this combination offers the complementary advantages of enhancing both the voiced and unvoiced regions. The DNN-based methods primarily rely on the network architecture, and hence, the prediction accuracy improves with the increasing complexity of the architecture. The lower complex models are essential for real-time processing systems. In this work, we propose a compact model using a sliding-window attention network (SWAN). The SWAN is trained to regress the spectral magnitude mask (SMM) from the noisy speech signal. Our experimental results demonstrate that the proposed approach achieves comparable performance with the state-of-the-art noncausal and causal speech enhancement methods with much lesser computational complexity. Our three-layered noncausal SWAN achieves 2.99 PESQ on the Valentini database with only 10 9 floating-point operations (FLOPs). © 2022, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.

In the present paper, we study the first and second order of accuracy difference schemes for the approximate solution of the inverse problem for hyperbolic–parabolic equations with unknown time-independent source term. The unique solvability of constructed difference schemes and the stability estimates for their solutions are obtained. The proofs are based on the spectral representation of the self-adjoint positive definite operator in a Hilbert space.

Recently, Kigami’s resistance form framework has been applied to provide a general approach for deriving the scaling limits of random walks on graphs with a fractal scaling limit (Croydon, Ann Inst Henri Poincaré Probab Stat 54(4):1939–1968, 2018; Croydon et al., Electron J Probab 22, paper no.82, 41, 2017). As an illustrative example, this article describes an application to the random conductance model with heavy tails on nested fractal graphs.

The paper deals with a zero-sum differential game in which the dynamical system is described by a fractional differential equation with the Caputo derivative of an order α∈ (0 , 1). The goal of the first (second) player is to minimize (maximize) a given quality index. The main contribution of the paper is the proof of the fact that this differential game has the value, i.e., the lower and upper game values coincide. The proof is based on the appropriate approximation of the game by a zero-sum differential game in which the dynamical system is described by a first-order functional differential equation of a retarded type. It is shown that the values of the approximating differential games have a limit, and this limit is the value of the original game. Moreover, the optimal players’ feedback control procedures are proposed that use the optimally controlled approximating system as a guide. An example is considered, and the results of computer simulations are presented. © 2019, Springer Science+Business Media, LLC, part of Springer Nature.

CRUE-CSIC (Acuerdos Transformativos 2022) Correction to: Milan J. Math. Vol. 90 (2022) 229–255, This paper concerns semilinear elliptic equations involving sign-changing weight function and a nonlinearity of subcritical nature understood in a generalized sense. Using an Orlicz–Sobolev space setting, we consider superlinear nonlinearities which do not have a polynomial growth, and state sufficient conditions guaranteeing the Palais–Smale condition. We study the existence of a bifurcated branch of classical positive solutions, containing a turning point, and providing multiplicity of solutions., Ministerio de Ciencia, Innovación y Universidades (España), Universidad Complutense de Madrid/Banco de Santander, Depto. de Análisis Matemático y Matemática Aplicada, Fac. de Ciencias Matemáticas, TRUE, pub

Gordan and Noether proved in their fundamental theorem that an hypersurface X= V(F) ⊆ Pn with n≤ 3 is a cone if and only if F has vanishing hessian (i.e. the determinant of the Hessian matrix). They also showed that the statement is false if n≥ 4 , by giving some counterexamples. Since their proof, several others have been proposed in the literature. In this paper we give a new one by using a different perspective which involves the study of standard Artinian Gorenstein K -algebras and the Lefschetz properties. As a further application of our setting, we prove that a standard Artinian Gorenstein algebra R= K[x, ⋯ , x4] / J with J generated by a regular sequence of quadrics has the strong Lefschetz property. In particular, this holds for Jacobian rings associated to smooth cubic threefolds.

End-to-end text-to-speech synthesis systems achieved immense success in recent times, with improved naturalness and intelligibility. However, the end-to-end models, which primarily depend on the attention-based alignment, do not offer an explicit provision to modify/incorporate the desired prosody while synthesizing the speech. Moreover, the state-of-the-art end-to-end systems use autoregressive models for synthesis, making the prediction sequential. Hence, the inference time and the computational complexity are quite high. This paper proposes Prosody-TTS, a data-efficient end-to-end speech synthesis model that combines the advantages of statistical parametric models and end-to-end neural network models. It also has a provision to modify or incorporate the desired prosody at the finer level by controlling the fundamental frequency (f) and the phone duration. Generating speech utterances with appropriate prosody and rhythm helps in improving the naturalness of the synthesized speech. We explicitly model the duration of the phoneme and the f to have a finer level control over them during the synthesis. The model is trained in an end-to-end fashion to directly generate the speech waveform from the input text, which in turn depends on the auxiliary subtasks of predicting the phoneme duration, f, and Mel spectrogram. Experiments on the Telugu language data of the IndicTTS database show that the proposed Prosody-TTS model achieves state-of-the-art performance with a mean opinion score of 4.08, with a very low inference time using just 4 hours of training data.

End-to-end text-to-speech synthesis systems achieved immense success in recent times, with improved naturalness and intelligibility. However, the end-to-end models, which primarily depend on the attention-based alignment, do not offer an explicit provision to modify/incorporate the desired prosody while synthesizing the speech. Moreover, the state-of-the-art end-to-end systems use autoregressive models for synthesis, making the prediction sequential. Hence, the inference time and the computational complexity are quite high. This paper proposes Prosody-TTS, a data-efficient end-to-end speech synthesis model that combines the advantages of statistical parametric models and end-to-end neural network models. It also has a provision to modify or incorporate the desired prosody at the finer level by controlling the fundamental frequency (f) and the phone duration. Generating speech utterances with appropriate prosody and rhythm helps in improving the naturalness of the synthesized speech. We explicitly model the duration of the phoneme and the f to have a finer level control over them during the synthesis. The model is trained in an end-to-end fashion to directly generate the speech waveform from the input text, which in turn depends on the auxiliary subtasks of predicting the phoneme duration, f, and Mel spectrogram. Experiments on the Telugu language data of the IndicTTS database show that the proposed Prosody-TTS model achieves state-of-the-art performance with a mean opinion score of 4.08, with a very low inference time using just 4 hours of training data.

Square-root unscented Kalman filter (SRUKF) is a widely used state estimator for several state of-the-art, highly nonlinear, and critical applications. It improves the stability and numerical accuracy of the system compared to the non-square root formulation, the unscented Kalman filter (UKF). At the same time, SRUKF is less computationally intensive compared to UKF, making it suitable for portable and battery-powered applications. This paper proposes a low-complexity and power-efficient architecture design methodology for SRUKF presented with a use case of the simultaneous localization and mapping (SLAM) problem. Implementation results show that the proposed SRUKF methodology is highly stable and achieves higher accuracy than the extensively used extended Kalman filter and UKF when developed for highly critical nonlinear applications such as SLAM. The design is synthesized and implemented on resource constraint Zynq-7000 XC7Z020 FPGA-based Zedboard development kit and compared with the state-of-the-art Kalman filter-based FPGA designs. Synthesis results show that the architecture is highly stable and has significant computation savings in DSP cores and clock cycles. The power consumption was reduced by 64 % compared to the state-of-the-art UKF design methodology. ASIC design was synthesized using UMC 90-nm technology, and the results for on-chip area and power consumption results have been discussed.

This paper is devoted to a mathematical analysis of some general models of mass transport and other coupled physical processes developed in simultaneous flows of surface, soil and ground waters. Such models are widely used for forecasting (numerical simulation) of a hydrological cycle for concrete territories. The mathematical models that proved a more realistic approach are obtained by combining several mathematical models for local processes. The water-exchange models take into account the following factors: Water flows in confined and unconfined aquifers, vertical moisture migration allowing earth surface evaporation, open-channel flow simulated by one-dimensional hydraulic equations, transport of contamination, etc. These models may have different levels of sophistication. We illustrate the type of mathematical singularities which may appear by considering a simple model on the coupling of a surface flow of surface and ground waters with the flow of a line channel or river., CMAF; University of Lisbon, Portugal, Secretaria de Estado de Universidades e Investigacion (Spain), DGISGPI, UCM/CM, Depto. de Análisis Matemático y Matemática Aplicada, Fac. de Ciencias Matemáticas, TRUE, pub

Homogeneous Riemannian structures have been studied and classified in terms of tensors through the works of Ambrose-Singer and of Tricerri-Vanhecke, dating back to the 1950s and 1980s, respectively. More recently, an abstract representation theoretic decomposition of the space V of tensors satisfying the symmetries of a homogeneous Riemannian structure has been proposed by A. Fino [Math. J. Toyama Univ. 21 (1998), 1–22; ] in the context of H-homogeneous structures, H being any of the possible irreducible holonomy groups. The paper under review deals with homogeneous quaternionic Kähler structures and its first result is a concrete description of the decomposition of V into five basic subspaces QK1,…,QK5 invariant under the action of Sp(n)⋅Sp(1), n≥2. Besides this decomposition, the main statements, anticipated in the note [M. Castrillón López, P. M. Gadea and A. Swann, C. R. Math. Acad. Sci. Paris 338 (2004), no. 1, 65–70; ], concern homogeneous quaternionic Kähler structures on the quaternionic hyperbolic space HHn. It is shown in particular that all such structures are in the class QK3 and that they are realized by the homogeneous models Sp(1)RN/Sp(1), where N is the nilpotent factor in the Iwasawa decomposition of Sp(n,1) and the isotropy representation depends on a positive real parameter., DGICYT, EDGE, Depto. de Álgebra, Geometría y Topología, Fac. de Ciencias Matemáticas, TRUE, pub

This paper puts together some techniques that have been previously developed by the authors,but separately, relative to fuzzy classification within a remote sensing setting. Considering that each image can be represented as a graph that defines proximity between pixels, certain distances between the characteristic of contiguous pixels are defined on such a graph, so a segmentation of the image into homogeneous regions can be produced by means of a particular algorithm. Such a segmentation can be then introduced as information, previously to any classification procedure, with an expected significative improvement. In particular, we consider specific measures in order to quantify such an improvement. This approach is being illustrated with its application into a particular land surface problem., TIN2006 - 06190, Depto. de Estadística e Investigación Operativa, Fac. de Ciencias Matemáticas, TRUE, pub

The study of overland flow of water over an erodible sediment leads to a coupled model describing the evolution of the topographic elevation and the depth of the overland water film. The spatially uniform solution of this model is unstable, and this instability corresponds to the formation of rills, which in reality then grow and coalesce to form large-scale river channels. In this paper we consider the deduction and mathematical analysis of a deterministic model describing river channel formation and the evolution of its depth. The model involves a degenerate nonlinear parabolic equation (satisfied on the interior of the support of the solution) with a super-linear source term and a prescribed constant mass. We propose here a global formulation of the problem (formulated in the whole space, beyond the support of the solution) which allows us to show the existence of a solution and leads to a suitable numerical scheme for its approximation. A particular novelty of the model is that the evolving channel self-determines its own width, without the need to pose any extra conditions at the channel margin., DGISGPI (Spain), Science Foundation Ireland, DGUIC, Depto. de Análisis Matemático y Matemática Aplicada, Fac. de Ciencias Matemáticas, TRUE, pub

In this paper we derive some similarity solutions of a nonlinear equation associated with a free boundary problem arising in the shallow-water approximation in glaciology. In addition we present a classical potential symmetry analysis of this second-order nonlinear degenerate parabolic equation related to non-Newtonian ice sheet dynamics in the isothermal case. After obtaining a general result connecting the thickness function of the ice sheet and the solution of the nonlinear equation (without any unilateral formulation), a particular example of a similarity solution to a problem formulated with Cauchy boundary conditions is described. This allows us to obtain several qualitative properties on the free moving boundary in the presence of an accumulation-ablation function with realistic physical properties., DGISGPI (Spain), DGUIC, Depto. de Análisis Matemático y Matemática Aplicada, Fac. de Ciencias Matemáticas, TRUE, pub

In this paper, we analyze the various strengthening and weakening of the uniqueness of the Hahn–Banach extension. In addition, we consider the case in which Y is an ideal of X. In this context, we study the property (U)/(SU)/(HB) and property (wU)/(k-U) for a subspace Y of a Banach space X. We obtain various new characterizations of these properties. We study different kinds of stabilities resulting from these properties in the tensor product spaces, spaces of Bochner integrable functions, and the higher duals of Banach spaces. We discuss various examples in the classical Banach spaces, where the aforementioned properties are satisfied and where they fail. It is established that a hyperplane in c has property (HB) if and only if it is an M-summand. It is observed that a finite-dimensional subspace Y has property (k-U) in c, in addition to that if Y is an ideal, then Y∗ is a k-strictly convex subspace of ℓ1 for some natural k.

In this paper, we analyze the various strengthening and weakening of the uniqueness of the Hahn–Banach extension. In addition, we consider the case in which Y is an ideal of X. In this context, we study the property (U)/(SU)/(HB) and property (wU)/(k-U) for a subspace Y of a Banach space X. We obtain various new characterizations of these properties. We study different kinds of stabilities resulting from these properties in the tensor product spaces, spaces of Bochner integrable functions, and the higher duals of Banach spaces. We discuss various examples in the classical Banach spaces, where the aforementioned properties are satisfied and where they fail. It is established that a hyperplane in c has property (HB) if and only if it is an M-summand. It is observed that a finite-dimensional subspace Y has property (k-U) in c, in addition to that if Y is an ideal, then Y∗ is a k-strictly convex subspace of ℓ1 for some natural k.

In this paper, we introduce a fragmented Huffman compression methodology for compressing convolution neural networks executing on edge devices. Present scenario demands deployment of deep networks on edge devices, since application needs to adhere to low latency, enhanced security and long-term cost effectiveness. However, the primary bottleneck lies in the expanded memory footprint on account of the large size of the neural net models. Existing software implementation of deep compression strategies do exist, where Huffman compression is applied on the quantized weights, reducing the deep neural network model size. However, there is a further possibility of compression in memory footprint from a hardware design perspective in edge devices, where our proposed methodology can be complementary to the existing strategies. With this motivation, we proposed a fragmented Huffman coding methodology, that can be applied to the binary equivalent of the numeric weights of a neural network model stored in device memor...

In an otherwise instructive 2012 article, Szilard provided a flawed argument purportedly establishing that the left (resp. right) Riemann sum of f(x) = 1/1+x^2 with respect to the uniform partition of [0,1] into n equal intervals is monotonically decreasing (resp. increasing) relative to n. A few years later, D. Borwein, J. M. Borwein and B. Sims developed a symmetrization technique that allowed them to provide a rectified proof that the right Riemann sum of f(x) = 1/1+x^2 really is monotonically increasing relative to n. They also provided numerical evidence suggesting that the left Riemann sum is decreasing but they did not succeed in proving it. In the first part of this paper, we exploit the symmetrization technique to provide a proof that the left Riemann sum is indeed decreasing with respect to n. Subsequently, we show, using elementary calculus techniques, some trigonometry computations as well as calculations involving generalized binomial coefficients, that the left and right Riemann sums with respect to the uniform partition of [0,1] of the family of functions of the form sin^p(pi x) are monotonically increasing relative to n, regardless of the value of p in (0,2). In so doing, we answer a problem that came up in the context of foundational research on questions situated at the intersection of matrix theory and metric geometry

In this paper, we analyze the various strengthening and weakening of the uniqueness of the Hahn–Banach extension. In addition, we consider the case in which Y is an ideal of X. In this context, we study the property (U)/(SU)/(HB) and property (wU)/(k-U) for a subspace Y of a Banach space X. We obtain various new characterizations of these properties. We study different kinds of stabilities resulting from these properties in the tensor product spaces, spaces of Bochner integrable functions, and the higher duals of Banach spaces. We discuss various examples in the classical Banach spaces, where the aforementioned properties are satisfied and where they fail. It is established that a hyperplane in c has property (HB) if and only if it is an M-summand. It is observed that a finite-dimensional subspace Y has property (k-U) in c, in addition to that if Y is an ideal, then Y∗ is a k-strictly convex subspace of ℓ1 for some natural k. © 2022, Tusi Mathematical Research Group (TMRG).

In this paper, we analyze the various strengthening and weakening of the uniqueness of the Hahn–Banach extension. In addition, we consider the case in which Y is an ideal of X. In this context, we study the property (U)/(SU)/(HB) and property (wU)/(k-U) for a subspace Y of a Banach space X. We obtain various new characterizations of these properties. We study different kinds of stabilities resulting from these properties in the tensor product spaces, spaces of Bochner integrable functions, and the higher duals of Banach spaces. We discuss various examples in the classical Banach spaces, where the aforementioned properties are satisfied and where they fail. It is established that a hyperplane in c has property (HB) if and only if it is an M-summand. It is observed that a finite-dimensional subspace Y has property (k-U) in c, in addition to that if Y is an ideal, then Y∗ is a k-strictly convex subspace of ℓ1 for some natural k. © 2022, Tusi Mathematical Research Group (TMRG).

In this paper, we analyze the various strengthening and weakening of the uniqueness of the Hahn–Banach extension. In addition, we consider the case in which Y is an ideal of X. In this context, we study the property (U)/(SU)/(HB) and property (wU)/(k-U) for a subspace Y of a Banach space X. We obtain various new characterizations of these properties. We study different kinds of stabilities resulting from these properties in the tensor product spaces, spaces of Bochner integrable functions, and the higher duals of Banach spaces. We discuss various examples in the classical Banach spaces, where the aforementioned properties are satisfied and where they fail. It is established that a hyperplane in c has property (HB) if and only if it is an M-summand. It is observed that a finite-dimensional subspace Y has property (k-U) in c, in addition to that if Y is an ideal, then Y∗ is a k-strictly convex subspace of ℓ1 for some natural k. © 2022, Tusi Mathematical Research Group (TMRG).

End-to-end text-to-speech synthesis systems achieved immense success in recent times, with improved naturalness and intelligibility. However, the end-to-end models, which primarily depend on the attention-based alignment, do not offer an explicit provision to modify/incorporate the desired prosody while synthesizing the speech. Moreover, the state-of-the-art end-to-end systems use autoregressive models for synthesis, making the prediction sequential. Hence, the inference time and the computational complexity are quite high. This paper proposes Prosody-TTS, a data-efficient end-to-end speech synthesis model that combines the advantages of statistical parametric models and end-to-end neural network models. It also has a provision to modify or incorporate the desired prosody at the finer level by controlling the fundamental frequency (f) and the phone duration. Generating speech utterances with appropriate prosody and rhythm helps in improving the naturalness of the synthesized speech. We explicitly model the duration of the phoneme and the f to have a finer level control over them during the synthesis. The model is trained in an end-to-end fashion to directly generate the speech waveform from the input text, which in turn depends on the auxiliary subtasks of predicting the phoneme duration, f, and Mel spectrogram. Experiments on the Telugu language data of the IndicTTS database show that the proposed Prosody-TTS model achieves state-of-the-art performance with a mean opinion score of 4.08, with a very low inference time using just 4 hours of training data. © 2022, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.

Gram–Schmidt orthogonalization is a popular fundamental technique of linear algebra, having wide-spread applications in state-of-the art and next-generation signal processing and communication technologies including Blind Source Separation, Independent Component Analysis, MIMO technology, Orthogonal Frequency Division Multiplexing, and QR Decomposition. On the other hand, Coordinate Rotation Digital Computer (CORDIC) is a technique being extensively used for the efficient implementation of complex arithmetic operations in various signal processing and communication modules. For all the aforementioned applications including FastICA and QR decomposition, CORDIC is being used widely for all the modules except GS where still costly multipliers, dividers, square root, and addition operations are being used. It motivated us to investigate the design for GS using CORDIC resulting in low-power and low-complex architecture of the entire design. In this paper, we propose a CORDIC-based low-complexity, low-power architecture design methodology for the n-dimensional GS algorithm where a single CORDIC unit can be re-used for implementation of several processing and communication modules on-chip. The proposed architecture precludes the use of additional arithmetic units to perform costly operations by recursive use of CORDIC, and thus significantly reduces its hardware complexity. The proposed architecture reduces the power consumption by 74–86% and the area by 12–40% for 3D to 6D GS, respectively, over the conventional approach. © 2021, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.

End-to-end text-to-speech synthesis systems achieved immense success in recent times, with improved naturalness and intelligibility. However, the end-to-end models, which primarily depend on the attention-based alignment, do not offer an explicit provision to modify/incorporate the desired prosody while synthesizing the speech. Moreover, the state-of-the-art end-to-end systems use autoregressive models for synthesis, making the prediction sequential. Hence, the inference time and the computational complexity are quite high. This paper proposes Prosody-TTS, a data-efficient end-to-end speech synthesis model that combines the advantages of statistical parametric models and end-to-end neural network models. It also has a provision to modify or incorporate the desired prosody at the finer level by controlling the fundamental frequency (f) and the phone duration. Generating speech utterances with appropriate prosody and rhythm helps in improving the naturalness of the synthesized speech. We explicitly model the duration of the phoneme and the f to have a finer level control over them during the synthesis. The model is trained in an end-to-end fashion to directly generate the speech waveform from the input text, which in turn depends on the auxiliary subtasks of predicting the phoneme duration, f, and Mel spectrogram. Experiments on the Telugu language data of the IndicTTS database show that the proposed Prosody-TTS model achieves state-of-the-art performance with a mean opinion score of 4.08, with a very low inference time using just 4 hours of training data. © 2022, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.

Gram–Schmidt orthogonalization is a popular fundamental technique of linear algebra, having wide-spread applications in state-of-the art and next-generation signal processing and communication technologies including Blind Source Separation, Independent Component Analysis, MIMO technology, Orthogonal Frequency Division Multiplexing, and QR Decomposition. On the other hand, Coordinate Rotation Digital Computer (CORDIC) is a technique being extensively used for the efficient implementation of complex arithmetic operations in various signal processing and communication modules. For all the aforementioned applications including FastICA and QR decomposition, CORDIC is being used widely for all the modules except GS where still costly multipliers, dividers, square root, and addition operations are being used. It motivated us to investigate the design for GS using CORDIC resulting in low-power and low-complex architecture of the entire design. In this paper, we propose a CORDIC-based low-complexity, low-power architecture design methodology for the n-dimensional GS algorithm where a single CORDIC unit can be re-used for implementation of several processing and communication modules on-chip. The proposed architecture precludes the use of additional arithmetic units to perform costly operations by recursive use of CORDIC, and thus significantly reduces its hardware complexity. The proposed architecture reduces the power consumption by 74–86% and the area by 12–40% for 3D to 6D GS, respectively, over the conventional approach. © 2021, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.

Gram–Schmidt orthogonalization is a popular fundamental technique of linear algebra, having wide-spread applications in state-of-the art and next-generation signal processing and communication technologies including Blind Source Separation, Independent Component Analysis, MIMO technology, Orthogonal Frequency Division Multiplexing, and QR Decomposition. On the other hand, Coordinate Rotation Digital Computer (CORDIC) is a technique being extensively used for the efficient implementation of complex arithmetic operations in various signal processing and communication modules. For all the aforementioned applications including FastICA and QR decomposition, CORDIC is being used widely for all the modules except GS where still costly multipliers, dividers, square root, and addition operations are being used. It motivated us to investigate the design for GS using CORDIC resulting in low-power and low-complex architecture of the entire design. In this paper, we propose a CORDIC-based low-complexity, low-power architecture design methodology for the n-dimensional GS algorithm where a single CORDIC unit can be re-used for implementation of several processing and communication modules on-chip. The proposed architecture precludes the use of additional arithmetic units to perform costly operations by recursive use of CORDIC, and thus significantly reduces its hardware complexity. The proposed architecture reduces the power consumption by 74–86% and the area by 12–40% for 3D to 6D GS, respectively, over the conventional approach. © 2021, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.

End-to-end text-to-speech synthesis systems achieved immense success in recent times, with improved naturalness and intelligibility. However, the end-to-end models, which primarily depend on the attention-based alignment, do not offer an explicit provision to modify/incorporate the desired prosody while synthesizing the speech. Moreover, the state-of-the-art end-to-end systems use autoregressive models for synthesis, making the prediction sequential. Hence, the inference time and the computational complexity are quite high. This paper proposes Prosody-TTS, a data-efficient end-to-end speech synthesis model that combines the advantages of statistical parametric models and end-to-end neural network models. It also has a provision to modify or incorporate the desired prosody at the finer level by controlling the fundamental frequency (f) and the phone duration. Generating speech utterances with appropriate prosody and rhythm helps in improving the naturalness of the synthesized speech. We explicitly model the duration of the phoneme and the f to have a finer level control over them during the synthesis. The model is trained in an end-to-end fashion to directly generate the speech waveform from the input text, which in turn depends on the auxiliary subtasks of predicting the phoneme duration, f, and Mel spectrogram. Experiments on the Telugu language data of the IndicTTS database show that the proposed Prosody-TTS model achieves state-of-the-art performance with a mean opinion score of 4.08, with a very low inference time using just 4 hours of training data. © 2022, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.

Gram–Schmidt orthogonalization is a popular fundamental technique of linear algebra, having wide-spread applications in state-of-the art and next-generation signal processing and communication technologies including Blind Source Separation, Independent Component Analysis, MIMO technology, Orthogonal Frequency Division Multiplexing, and QR Decomposition. On the other hand, Coordinate Rotation Digital Computer (CORDIC) is a technique being extensively used for the efficient implementation of complex arithmetic operations in various signal processing and communication modules. For all the aforementioned applications including FastICA and QR decomposition, CORDIC is being used widely for all the modules except GS where still costly multipliers, dividers, square root, and addition operations are being used. It motivated us to investigate the design for GS using CORDIC resulting in low-power and low-complex architecture of the entire design. In this paper, we propose a CORDIC-based low-complexity, low-power architecture design methodology for the n-dimensional GS algorithm where a single CORDIC unit can be re-used for implementation of several processing and communication modules on-chip. The proposed architecture precludes the use of additional arithmetic units to perform costly operations by recursive use of CORDIC, and thus significantly reduces its hardware complexity. The proposed architecture reduces the power consumption by 74–86% and the area by 12–40% for 3D to 6D GS, respectively, over the conventional approach. © 2021, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.

Gram–Schmidt orthogonalization is a popular fundamental technique of linear algebra, having wide-spread applications in state-of-the art and next-generation signal processing and communication technologies including Blind Source Separation, Independent Component Analysis, MIMO technology, Orthogonal Frequency Division Multiplexing, and QR Decomposition. On the other hand, Coordinate Rotation Digital Computer (CORDIC) is a technique being extensively used for the efficient implementation of complex arithmetic operations in various signal processing and communication modules. For all the aforementioned applications including FastICA and QR decomposition, CORDIC is being used widely for all the modules except GS where still costly multipliers, dividers, square root, and addition operations are being used. It motivated us to investigate the design for GS using CORDIC resulting in low-power and low-complex architecture of the entire design. In this paper, we propose a CORDIC-based low-complexity, low-power architecture design methodology for the n-dimensional GS algorithm where a single CORDIC unit can be re-used for implementation of several processing and communication modules on-chip. The proposed architecture precludes the use of additional arithmetic units to perform costly operations by recursive use of CORDIC, and thus significantly reduces its hardware complexity. The proposed architecture reduces the power consumption by 74–86% and the area by 12–40% for 3D to 6D GS, respectively, over the conventional approach. © 2021, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.

In this paper we prove the convergence of solutions to discrete models for binary waveguide arrays toward those of their formal continuum limit, for which we also show the existence of localized standing waves. This work rigorously justifies formal arguments and numerical simulations present in the Physics literature.

© 2016, Springer Science+Business Media New York.Discrete fractional Fourier transform (DFrFT) is a powerful signal processing tool. This paper proposes a method for DFrFT-based image retrieval via Fisher discriminant and 1-NN classification rule. First, this paper proposes to extend the conventional discrete Fourier transform (DFT) descriptors to the DFrFT descriptors to be used for representing the edges of images. The DFrFT descriptors extracted from the training images are employed to construct a dictionary, for which the corresponding optimal rotational angles of the DFrFTs are required to be determined. This dictionary design problem is formulated as an optimization problem, where the Fisher discriminant is the objective function to be minimized. This optimization problem is nonconvex (Guan et al. in IEEE Trans Image Process 20(7):2030–2048, 2011; Ho et al. in IEEE Trans Signal Process 58(8):4436–4441, 2010). Furthermore, both the intraclass separation and interclass separation of the DFrFT descriptors are independent of the rotational angles if these separations are defined in terms of the 2-norm operator. To tackle these difficulties, the 1-norm operator is employed. However, this reformulated optimization problem is nonsmooth. To solve this problem, the nondifferentiable points of the objective function are found. Then, the stationary points between any two consecutive nondifferentiable points are identified. The objective function values are evaluated at these nondifferentiable points and these stationary points. The smallest L objective function values are picked up and the corresponding rotational angles are determined, which are then used to construct the dictionary. Here, L is the total number of the rotational angles of the DFrFTs used to construct the dictionary. Finally, an 1-NN classification rule is applied to perform the image retrieval. Application examples and experimental results show that our proposed method outperforms the conventional DFT a

In heritage conservation, a gap is often observed between the theory of conservation as a durable process that aims at the preservation of a historic building and the practice of restoration as a single intervention that aims at a fast and convincing result. This paper describes the proposed approach for the conservation of the main façade of the Shoemakers Chapel (in Dutch: Schoenmakerskapel) in Antwerp (Belgium), a listed monument since 1976. It serves as an example of how to develop a durable and realistic approach for the conservation of a sixteenth century façade. The basis for the conservation approach is the understanding that each intervention should take the stratified significance of the historic façade into account. In this paper, it will be shown how to combine a study of the façade from a technical point of view with an analysis of the façade as a carrier of cultural significance.

In heritage conservation, a gap is often observed between the theory of conservation as a durable process that aims at the preservation of a historic building and the practice of restoration as a single intervention that aims at a fast and convincing result. This paper describes the proposed approach for the conservation of the main façade of the Shoemakers Chapel (in Dutch: Schoenmakerskapel) in Antwerp (Belgium), a listed monument since 1976. It serves as an example of how to develop a durable and realistic approach for the conservation of a sixteenth century façade. The basis for the conservation approach is the understanding that each intervention should take the stratified significance of the historic façade into account. In this paper, it will be shown how to combine a study of the façade from a technical point of view with an analysis of the façade as a carrier of cultural significance.

Convolutional neural network (CNN) is one of the most dominant deep learning networks with good generalization ability. Its high performance in solving large and complex learning problems has enabled usability in IoT devices. However, CNN involves a substantial amount of convolution operations, which demand a large number of power-consuming multipliers. This hinders the deployment of deep CNNs on mobile and IoT edge devices owing to restricted power–area constraints. In this paper, we propose a low-complex methodology named ‘minimal modified distributed arithmetic’ (M2DA) for convolutional neural network (CNN) by exploiting the data symmetry and consequently storing only the unique kernel coefficient’s combinations and the size of required memory and multiplication operations can be reduced, leading to power–area efficient design. For validation, a low-complex CNN architecture for activity recognition application is designed and synthesized in Synopsys using the UMC 65 nm technology wherein average 36.89% and 51.63% improvement is achieved in power and area, respectively, compared to conventional MDA methodology. To demonstrate the significance of the proposed M2DA methodology, we have also implemented the Alexnet which is the most widely and publicly available CNN model for the image classification problem.

Producción Científica, In this paper, we study the algebraic, rational and formal Puiseux series solutions of certain type of systems of autonomous ordinary differential equations. More precisely, we deal with systems which associated algebraic set is of dimension one. We establish a relationship between the solutions of the system and the solutions of an associated first order autonomous ordinary differential equation, that we call the reduced differential equation. Using results on such equations, we prove the convergence of the formal Puiseux series solutions of the system, expanded around a finite point or at infinity, and we present an algorithm to describe them. In addition, we bound the degree of the possible algebraic and rational solutions, and we provide an algorithm to decide their existence and to compute such solutions if they exist. Moreover, if the reduced differential equation is non trivial, for every given point (x, y) ∈ C2, we prove the existence of a convergent Puiseux series solution y(x) of the original system such that y(x) = y. © 2020, The Author(s)., Ministerio de Economía, Industria y Competitividad, AEI, FEDER, Grant MTM2016-77642-C2-1-P, FEDER/Ministerio de Ciencia, Innovación y Universidades Agencia Estatal de Investigación/MTM2017-88796-P, Austrian Science Fund (FWF): P 31327-N32, Open access funding provided by Johannes Kepler University Linz

This paper deals with the possibility of transforming a weakly measurable function in a Hilbert space into a continuous frame by a metric operator, i.e., a strictly positiveself-adjoint operator. A necessary condition is that the domain of the analysis operator associated to the function be dense. The study is done also with the help of the generalized frame operator associated to a weakly measurable function, which has better properties than the usual frame operator. A special attention is given to lower semi-frames: indeed if the domain of the analysis operator is dense, then a lower semi-frame can be transformed into a Parseval frame with a (special) metric operator.

For a stochastic difference equation D n = A n D n−1 + B n which stabilises upon time we study tail distribution asymptotics for D n under the assumption that the distribution of log(1+|A1|+|B1|) is heavy-tailed, that is, all its positive exponential moments are infinite. The aim of the present paper is three-fold. Firstly, we identify the asymptotic behaviour not only of the stationary tail distribution but also of D n. Secondly, we solve the problem in the general setting when A takes both positive and negative values. Thirdly, we get rid of auxiliary conditions like finiteness of higher moments introduced in the literature before.

Convolutional neural network (CNN) is one of the most dominant deep learning networks with good generalization ability. Its high performance in solving large and complex learning problems has enabled usability in IoT devices. However, CNN involves a substantial amount of convolution operations, which demand a large number of power-consuming multipliers. This hinders the deployment of deep CNNs on mobile and IoT edge devices owing to restricted power–area constraints. In this paper, we propose a low-complex methodology named ‘minimal modified distributed arithmetic’ (M2DA) for convolutional neural network (CNN) by exploiting the data symmetry and consequently storing only the unique kernel coefficient’s combinations and the size of required memory and multiplication operations can be reduced, leading to power–area efficient design. For validation, a low-complex CNN architecture for activity recognition application is designed and synthesized in Synopsys using the UMC 65 nm technology wherein average 36.89% and 51.63% improvement is achieved in power and area, respectively, compared to conventional MDA methodology. To demonstrate the significance of the proposed M2DA methodology, we have also implemented the Alexnet which is the most widely and publicly available CNN model for the image classification problem.

Convolutional neural network (CNN) is one of the most dominant deep learning networks with good generalization ability. Its high performance in solving large and complex learning problems has enabled usability in IoT devices. However, CNN involves a substantial amount of convolution operations, which demand a large number of power-consuming multipliers. This hinders the deployment of deep CNNs on mobile and IoT edge devices owing to restricted power–area constraints. In this paper, we propose a low-complex methodology named ‘minimal modified distributed arithmetic’ (M2DA) for convolutional neural network (CNN) by exploiting the data symmetry and consequently storing only the unique kernel coefficient’s combinations and the size of required memory and multiplication operations can be reduced, leading to power–area efficient design. For validation, a low-complex CNN architecture for activity recognition application is designed and synthesized in Synopsys using the UMC 65 nm technology wherein average 36.89% and 51.63% improvement is achieved in power and area, respectively, compared to conventional MDA methodology. To demonstrate the significance of the proposed M2DA methodology, we have also implemented the Alexnet which is the most widely and publicly available CNN model for the image classification problem.

Convolutional neural network (CNN) is one of the most dominant deep learning networks with good generalization ability. Its high performance in solving large and complex learning problems has enabled usability in IoT devices. However, CNN involves a substantial amount of convolution operations, which demand a large number of power-consuming multipliers. This hinders the deployment of deep CNNs on mobile and IoT edge devices owing to restricted power–area constraints. In this paper, we propose a low-complex methodology named ‘minimal modified distributed arithmetic’ (M2DA) for convolutional neural network (CNN) by exploiting the data symmetry and consequently storing only the unique kernel coefficient’s combinations and the size of required memory and multiplication operations can be reduced, leading to power–area efficient design. For validation, a low-complex CNN architecture for activity recognition application is designed and synthesized in Synopsys using the UMC 65 nm technology wherein average 36.89% and 51.63% improvement is achieved in power and area, respectively, compared to conventional MDA methodology. To demonstrate the significance of the proposed M2DA methodology, we have also implemented the Alexnet which is the most widely and publicly available CNN model for the image classification problem.

Convolutional neural network (CNN) is one of the most dominant deep learning networks with good generalization ability. Its high performance in solving large and complex learning problems has enabled usability in IoT devices. However, CNN involves a substantial amount of convolution operations, which demand a large number of power-consuming multipliers. This hinders the deployment of deep CNNs on mobile and IoT edge devices owing to restricted power–area constraints. In this paper, we propose a low-complex methodology named ‘minimal modified distributed arithmetic’ (M2DA) for convolutional neural network (CNN) by exploiting the data symmetry and consequently storing only the unique kernel coefficient’s combinations and the size of required memory and multiplication operations can be reduced, leading to power–area efficient design. For validation, a low-complex CNN architecture for activity recognition application is designed and synthesized in Synopsys using the UMC 65 nm technology wherein average 36.89% and 51.63% improvement is achieved in power and area, respectively, compared to conventional MDA methodology. To demonstrate the significance of the proposed M2DA methodology, we have also implemented the Alexnet which is the most widely and publicly available CNN model for the image classification problem.

Convolutional neural network (CNN) is one of the most dominant deep learning networks with good generalization ability. Its high performance in solving large and complex learning problems has enabled usability in IoT devices. However, CNN involves a substantial amount of convolution operations, which demand a large number of power-consuming multipliers. This hinders the deployment of deep CNNs on mobile and IoT edge devices owing to restricted power–area constraints. In this paper, we propose a low-complex methodology named ‘minimal modified distributed arithmetic’ (M2DA) for convolutional neural network (CNN) by exploiting the data symmetry and consequently storing only the unique kernel coefficient’s combinations and the size of required memory and multiplication operations can be reduced, leading to power–area efficient design. For validation, a low-complex CNN architecture for activity recognition application is designed and synthesized in Synopsys using the UMC 65 nm technology wherein average 36.89% and 51.63% improvement is achieved in power and area, respectively, compared to conventional MDA methodology. To demonstrate the significance of the proposed M2DA methodology, we have also implemented the Alexnet which is the most widely and publicly available CNN model for the image classification problem.

For a stochastic difference equation D n = A n D n−1 + B n which stabilises upon time we study tail distribution asymptotics for D n under the assumption that the distribution of log(1+|A1|+|B1|) is heavy-tailed, that is, all its positive exponential moments are infinite. The aim of the present paper is three-fold. Firstly, we identify the asymptotic behaviour not only of the stationary tail distribution but also of D n. Secondly, we solve the problem in the general setting when A takes both positive and negative values. Thirdly, we get rid of auxiliary conditions like finiteness of higher moments introduced in the literature before.