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In this paper, we initiate the study of enriched ρ-nonexpansive mappings in modular function spaces. First we show that in modular function spaces, every ρ-nonexpansive mapping is enriched ρ-nonexpansive mapping but not conversely and that their sets of fixed point are same. Next, we prove a ρ-convergence result on approximation of fixed points of enriched ρ-nonexpansive mappings in modular function spaces. We verify the validity of the result by an example. We construct a table to show our findings. Finally, we give one more ρ-convergence result under different conditions. Our results are new for ρ-nonexpansive mappings in modular function spaces. [ABSTRACT FROM AUTHOR]

In this paper, we study the budget-constrained profit maximization problem with expensive seed endorsement, a derivation of the well-studied influence maximization and profit maximization in social networks. While existing research requires the non-negativity of the objective profit function, this paper considers real-world scenarios where costs may surpass revenue. Specifically, our problem can be regarded as maximizing the difference between a non-negative submodular function and a non-negative modular function under a knapsack constraint, allowing for negative differences. To tackle this challenge, we propose two algorithms. Firstly, we employ a twin greedy and enumeration technique to design a polynomial-time algorithm with a quarter weak approximation ratio, providing a balance between computational efficiency and solution quality. Then, we incorporate a threshold decreasing technique to enhance the time complexity of the first algorithm, yielding an improved computational efficiency while maintaining a reasonable level of solution accuracy. To our knowledge, this is the first paper to study the profit maximization beyond non-negativity and to propose polynomial-time algorithms with a constant bicriteria approximation ratio. [ABSTRACT FROM AUTHOR]

Gukov–Pei–Putrov–Vafa conjectured the existence of q -series whose radial limits are Witten–Reshetikhin–Turaev invariants and called them homological blocks. For weakly negative definite plumbed 3-manifolds, Gukov–Pei–Putrov–Vafa and Gukov–Manolescu constructed homological blocks. In this paper, we construct indefinite false theta functions which are candidates of homological blocks for some plumbed 3 -manifolds which are not weakly negative definite. Moreover we prove that, for the Poincaré homology sphere, our indefinite false theta function coincides with the original homological block. [ABSTRACT FROM AUTHOR]

An AC (alternative current) power integration of distributed energies faces multi-fold challenges such as synchronization and weak grid-induced instability. In this study, a multi-terminal DC transformer is proposed for renewable energy clusters grid connection. The DC transformer provides multiple DC input ports for renewable energy collection, while the load port is connected to the medium-voltage DC grid via a modular multilevel converter (MMC). The multi-port topology enables flexible power transfer between multiple input sources to the load without additional components. The carrier layer modulation strategy is implemented to balance the MMC module voltage; bidirectional power transmission between multiple input sources is achieved through the phase shift modulation (PSM) method. First, we provided a detailed introduction of the proposed topology and working principle. A simulation model was built using the SIMULINK, and the simulation results verified the effectiveness of the proposed converter modulation strategy and phase shift modulation method. A corresponding hardware experimental platform was designed and built, and the modulation and voltage equalization functions of modular multilevel rectifiers were presented as well as the measured results of power transmission modulation of the converter under single-input and multi-input conditions. The results indicate that the proposed transformer can achieve multiple DC inputs and has multi-channel power transmission capabilities, making it suitable for renewable energy clusters grid connection. [ABSTRACT FROM AUTHOR]

Ranks of partitions play an important role in the theory of partitions. They provide combinatorial interpretations for Ramanujan's famous congruences for partition functions. We establish a family of congruences modulo powers of $5$ for ranks of partitions. [ABSTRACT FROM AUTHOR]

In this paper, a predetermined performance controller is proposed for a modular charging system for electric vehicles to solve the problem that the entering and leaving of electric vehicles will cause large voltage fluctuation, which will affect the service life of the battery. A barrier Lyapunov function is introduced and combined with the backstepping method to design the controller to ensure that the output voltage of the system can be limited to a set range. The entering and leaving of electric vehicles will result in changes in the system's load, however, this change is unknown, so a finite-time load estimator is designed to estimate the load variation. Then the estimated load is introduced into the controller to improve the adaptive ability of the controller. [ABSTRACT FROM AUTHOR]

A plethora of investigations have been carried out in studying inequalities for the Fourier coefficients of weakly holomorphic modular forms, for example, the partition function. Recently, Bringmann, Kane, Rolen, and Tripp studied asymptotics for the k-colored partition function and more generally, for the fractional partitions arising from the Nekrasov-Okounkov formula which in turn allowed them to prove generalized multiplicative inequalities. Motivated by their idea to find interesting inequalities for the k-colored partition functions, denoted by p k (n) , in this paper, we prove a family of inequalities for the p 24 (n) . The main aim of this paper is to study the asymptotic expansion with an effective estimate for the error bound regarding the Fourier coefficients of the modular form 1 / Δ (up to a constant c and a power of q), where Δ is the modular discriminant function and a well-known combinatorial interpretation for the associated coefficient sequence is called 24-colored partitions, denoted by p 24 (n) . Consequently, we show that p 24 (n) satisfies 2- log -concavity, Turán inequality of order 3, and Laguerre inequalities of order m with 2 ≤ m ≤ 8 eventually. Our method of estimations for the error term of the asymptotic expansion for p 24 (n) can be adapted in a more general paradigm where the Fourier coefficients of a certain class of Dedekind-eta quotients which are essentially a modular form of negative weight, admit a Rademacher type exact formula involving the I-Bessel function of positive order. [ABSTRACT FROM AUTHOR]

A comparison and analysis of using the developed software implementation of the MontgomeryArithmetic class for computing modular exponentiation are conducted. The performance speed of the developed Montgomery modular multiplication is compared to that of the regular modular multiplication for calculating the modular exponentiation based on the right-to-left binary method for a fixed basis with precomputation of a reduced set of residues. The obtained results of modular exponentiation computing with parallelization based on multithreading on general-purpose computers speed up the computation by an average of 1.5 times using the developed modular Montgomery multiplication compared to the modular exponentiation functions of the MPIR, OpenSSL, and Crypto++ software libraries. [ABSTRACT FROM AUTHOR]

We consider a Dirichlet problem driven by the anisotropic (p , q) Laplacian. In the reaction, we have a parametric partially concave term plus a "superlinear" perturbation (convex term) which need not satisfy the Ambrosetti–Rabinowitz condition. Using variational tools, we show that for all small values of the parameter λ > 0 , the problem has at least two nontrivial smooth solutions. [ABSTRACT FROM AUTHOR]

A comparison and analysis of the use of the developed software implementation of the class MontgomeryArithmetic for computing modular exponentiation are conducted. The computation speed of the developed Montgomery modular multiplication is compared to the regular modular multiplication for calculating the modular exponentiation based on the right-to-left binary elevation method for a fixed basis with a preliminary calculation of a reduced set of remainders. The obtained results of performing modular exponentiation computations with parallelization based on multithreading on general-purpose computers speed up the computations by an average of 1.5 times using the developed modular Montgomery multiplication compared to the modular exponentiation functions of the MPIR, OpenSSL, and Crypto++ software libraries. [ABSTRACT FROM AUTHOR]

In this paper, we construct generalized L-functions associated to meromorphic modular forms of weight 1 2 for the theta group with a single simple pole in the fundamental domain. We then consider their behavior toward i∞ and relate this to the Riemann zeta function. [ABSTRACT FROM AUTHOR]

Copyright of Telecommunication Engineering is the property of Telecommunication Engineering and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

In function fields in positive characteristic, we provide a concrete example of completely normal elements for a finite Galois extension. More precisely, for a nonabelian extension, we construct completely normal elements for Drinfeld modular function fields using Siegel functions in function fields. For an abelian extension, we construct completely normal elements for cyclotomic function fields. [ABSTRACT FROM AUTHOR]

Elsner, Luca and Tachiya proved in [4] that the values of the Jacobi-theta constants θ 3 (m τ) and θ 3 (n τ) are algebraically independent over Q for distinct integers m , n under some conditions on τ . On the other hand, in [3] Elsner and Tachiya also proved that three values θ 3 (m τ) , θ 3 (n τ) and θ 3 (ℓ τ) are algebraically dependent over Q . In this article we prove the non-vanishing of linear forms in θ 3 (m τ) , θ 3 (n τ) and θ 3 (ℓ τ) under various conditions on m , n , ℓ , and τ . Among other things we prove that for odd and distinct positive integers m , n > 3 the three numbers θ 3 (τ) , θ 3 (m τ) and θ 3 (n τ) are linearly independent over Q ¯ when τ is an algebraic number of some degree greater or equal to 3. In some sense this fills the gap between the above-mentioned former results on theta constants. A theorem on the linear independence over C (τ) of the functions θ 3 (a 1 τ) , ⋯ , θ 3 (a m τ) for distinct positive rational numbers a 1 , ⋯ , a m is also established. [ABSTRACT FROM AUTHOR]

Endoscopes are crucial for assisting in surgery and disease diagnosis, including the early detection of cancer. The effective use of endoscopes relies on their optical performance, which can be characterized with a series of metrics such as resolution, vital for revealing anatomical details. The modulation transfer function (MTF) is a key metric for evaluating endoscope resolution. However, the 2020 version of the ISO 8600-5 standard, while introducing an endoscope MTF measurement method, lacks empirical validation and excludes opto-electronic video endoscopes, the largest family of endoscopes. Measuring the MTF of video endoscopes requires tailored standards that address their unique characteristics. This paper aims to expand the scope of ISO 8600-5:2020 to include video endoscopes, by optimizing the MTF test method and addressing parameters affecting measurement accuracy. We studied the effects of intensity and uniformity of image luminance, chart modulation compensation, linearity of image digital values, auto gain control, image enhancement, image compression and the region of interest dimensions on images of slanted-edge test charts, and thus the MTF based on these images. By analyzing these effects, we provided recommendations for setting and controlling these factors to obtain accurate MTF curves. Our goal is to enhance the standard's relevance and effectiveness for measuring the MTF of a broader range of endoscopic devices, with potential applications in the MTF measurement of other digital imaging devices. [ABSTRACT FROM AUTHOR]

This study looks closely into the analysis of the variation of constants formula given by Φ (t) = S (t) Φ (0) + ∫ 0 t S (t − σ) F (σ , Φ (σ)) d σ , for t ∈ [ 0 , T ] , T > 0 , within the context of modular function spaces L ρ . Additionally, this research explores practical applications of the variation of constants formula in variable exponent Lebesgue spaces L p (·) . Specifically, the study examines these spaces under certain conditions applied to the exponent function p (·) and the functions F as well as the semigroup S (t) , utilizing the symmetry properties of the algebraic semigroup. This investigation sheds light on the intricate interplay between parameters and functions within these mathematical frameworks, offering valuable insights into their behavior and properties in L p (·) . [ABSTRACT FROM AUTHOR]

The aim of this paper is to introduce the cyclic-Fibonacci hybrid sequence and give some properties. By taking into account the cyclic-Fibonacci hybrid sequence modulo m, the method will be given to determine the period lengths of this sequence according to the different m values. In the final part of this paper, we study the cyclic-Fibonacci hybrid sequence in groups and then we calculate the cyclic-Fibonacci hybrid lengths of polyhedral groups (2; 2; 2), (2; n; 2) and (n; 2; 2) as applications of the results produced. [ABSTRACT FROM AUTHOR]

By using modular functions on the upper complex half-plane, we study a class of strain energies for crystalline materials whose global invariance originates from the full symmetry group of the underlying lattice. This follows Ericksen's suggestion which aimed at extending the Landau-type theories to encompass the behavior of crystals undergoing structural phase transformation, with twinning, microstructure formation, and possibly associated plasticity effects. Here we investigate such Ericksen-Landau strain energies for the modelling of reconstructive transformations, focusing on the prototypical case of the square-hexagonal phase change in 2D crystals. We study the bifurcation and valley-floor network of these potentials, and use one in the simulation of a quasi-static shearing test. We observe typical effects associated with the micro-mechanics of phase transformation in crystals, in particular, the bursty progress of the structural phase change, characterized by intermittent stress-relaxation through microstructure formation, mediated, in this reconstructive case, by defect nucleation and movement in the lattice. [ABSTRACT FROM AUTHOR]

The applicability of the distance aggregation problem has attracted the interest of many authors. Motivated by this fact, in this paper, we face the modular quasi-(pseudo-)metric aggregation problem, which consists of analyzing the properties that a function must have to fuse a collection of modular quasi-(pseudo-)metrics into a single one. In this paper, we characterize such functions as monotone, subadditive and vanishing at zero. Moreover, a description of such functions in terms of triangle triplets is given, and, in addition, the relationship between modular quasi-(pseudo-)metric aggregation functions and modular (pseudo-)metric aggregation functions is discussed. Specifically, we show that the class of modular (quasi-)(pseudo-)metric aggregation functions coincides with that of modular (pseudo-)metric aggregation functions. The characterizations are illustrated with appropriate examples. A few methods to construct modular quasi-(pseudo-)metrics are provided using the exposed theory. By exploring the existence of absorbent and neutral elements of modular quasi-(pseudo-)metric aggregation functions, we find that every modular quasi-pseudo-metric aggregation function with 0 as the neutral element is an Aumann function, is majored by the sum and satisfies the 1-Lipschitz condition. Moreover, a characterization of those modular quasi-(pseudo-)metric aggregation functions that preserve modular quasi-(pseudo-)metrics is also provided. Furthermore, the relationship between modular quasi-(pseudo-)metric aggregation functions and quasi-(pseudo-)metric aggregation functions is studied. Particularly, we have proven that they are the same only when the former functions are finite. Finally, the usefulness of modular quasi-(pseudo-)metric aggregation functions in multi-agent systems is analyzed. [ABSTRACT FROM AUTHOR]

This paper presents a dynamic-phasor-based, average-value modeling method for power systems with extensive converter-tied subsystems. In the proposed approach, the overall system model is constructed using modular functions, interfacing both conventional and converter-tied resources. Model validation is performed against detailed Electro-Magnetic Transient (EMT) simulations. The analytical capabilities offered by the proposed modeling method are demonstrated on a modified IEEE 9-bus system. A Graphics Processing Unit (GPU)-based parallel computing approach for the solution of the resulting model is presented and exemplified on a modified IEEE 118-bus system, showing significant improvements in computing efficiency over EMT solvers. A co-simulation approach using a Central Processing Unit (CPU) and a GPU is also presented and exemplified using a modified version of the IEEE 118-bus system, demonstrating the model's parallelization. [ABSTRACT FROM AUTHOR]

In this paper, we present a thorough study of the regularized submodular maximization problem, in which the objective $ f:=g-\ell $ f := g − ℓ can be expressed as the difference between a submodular function and a modular function. This problem has drawn much attention in recent years. While existing works focuses on the case of g being monotone, we investigate the problem with a nonmonotone g. The main technique we use is to introduce a distorted objective function, which varies weights of the submodular component g and the modular component ℓ during the iterations of the algorithm. By combining the weighting technique and measured continuous greedy algorithm, we present an algorithm for the matroid-constrained problem, which has a provable approximation guarantee. In the cardinality-constrained case, we utilize random greedy algorithm and sampling technique together with the weighting technique to design two efficient algorithms. Moreover, we consider the unconstrained problem and propose a much simpler and faster algorithm compared with the algorithms for solving the problem with a cardinality constraint. [ABSTRACT FROM AUTHOR]

We study the Wilson line defect half-indices of 3d N = 2 supersymmetric SU(N) Chern-Simons theories of level k ≤ – N with Neumann boundary conditions for the gauge fields, together with 2d Fermi multiplets and fundamental 3d chiral multiplets to cancel the gauge anomaly. We derive some exact results and also make some conjectures based on expansions of the q-series. We find several interesting connections with special functions known in the literature, including Rogers-Ramanujan functions for which we conjecture integral representations, and the appearance of Appell-Lerch sums for certain Wilson line half-index grand canonical ensembles which reveal an unexpected appearance of mock modular functions. We also find intriguing q-difference equations relating half-indices to Wilson line half-indices. Some of these results also have a description in terms of a dual theory with Dirichlet boundary conditions for the vector multiplet in the dual theory. [ABSTRACT FROM AUTHOR]

In this paper, we present a five-step iterative scheme, at the beginning, it seems complicated and difficult to implement, but in fact it’s not. This scheme is constructed for (λ,ρ) - firmly nonexpansive mappings in modular function spaces. Two different ρ-convergences result has been proved for double schemes under consideration. In our study there is a comparison between these cases through answering the question "which one is faster?” Finally, numerical examples are given by using MATLAB software program. [ABSTRACT FROM AUTHOR]

Our results investigate mock theta functions and quantum modular forms via quantum q-series identities. After Lovejoy, quantum q-series identities are such that they do not hold as an equality between power series inside the unit disc in the classical sense, but do hold at dense sets of roots of unity on the boundary. We establish several general (multivariable) quantum q-series identities and apply them to various settings involving (universal) mock theta functions. As a consequence, we surprisingly show that limiting, finite, universal mock theta functions at roots of unity for which their infinite counterparts do not converge are quantum modular. Moreover, we show that these finite limiting universal mock theta functions play key roles in (generalized) Ramanujan radial limits. A further corollary of our work reveals that the finite Kontsevich–Zagier series is a kind of "universal quantum mock theta function," in that it may be used to evaluate odd-order Ramanujan mock theta functions at roots of unity. (We also offer a similar result for even-order mock theta functions.) Finally, to complement the notion of a quantum q-series identity and the results of this paper, we also define what we call an "antiquantum q-series identity' and offer motivating general results with applications to third-order mock theta functions. [ABSTRACT FROM AUTHOR]

In this work, we present a new weighted method for proving the generalized Hyers-Ulam stability for nonlinear Volterra integral equations in modular spaces. Using the same technique, we also prove the generalized Hyers-Ulam stability for nonlinear functional equations under Δ2 conditions. Fixed-point theorems in modular spaces form the foundation of our main conclusions. [ABSTRACT FROM AUTHOR]

Distributed maximization of a submodular function in the MapReduce (MR) model has received much attention, culminating in two frameworks that allow a centralized algorithm to be run in the MR setting without loss of approximation, as long as the centralized algorithm satisfies a certain consistency property – which had previously only been known to be satisfied by the standard greedy and continous greedy algorithms. A separate line of work has studied parallelizability of submodular maximization in the adaptive complexity model, where each thread may have access to the entire ground set. For the size-constrained maximization of a monotone and submodular function, we show that several sublinearly adaptive (highly parallelizable) algorithms satisfy the consistency property required to work in the MR setting, which yields practical, parallelizable and distributed algorithms. Separately, we develop the first distributed algorithm with linear query complexity for this problem. Finally, we provide a method to increase the maximum cardinality constraint for MR algorithms at the cost of additional MR rounds. [ABSTRACT FROM AUTHOR]

We show that for every finite set of prime numbers $S$ , there are at most finitely many singular moduli that are $S$ -units. The key new ingredient is that for every prime number $p$ , singular moduli are $p$ -adically disperse. We prove analogous results for the Weber modular functions, the $\lambda$ -invariants and the McKay–Thompson series associated with the elements of the monster group. Finally, we also obtain that a modular function that specializes to infinitely many algebraic units at quadratic imaginary numbers must be a weak modular unit. [ABSTRACT FROM AUTHOR]

The Petersson inner product is a natural inner product on the space of modular invariant functions. We derive a formula, written as a convergent sum over elementary functions, for the inner product Es(G, B) of the real analytic Eisenstein series and a general point in Narain moduli space. We also discuss the utility of the Petersson inner product as a distance measure on the space of 2d CFTs, and apply our procedure to evaluate this distance in various examples. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Harbin University of Science & Technology is the property of Journal of Harbin University of Science & Technology and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Prime factorization is a procedure of determining the prime factors of a given number N that requires super-polynomial time for conventional digital computers. Peter Shor developed a polynomial-time algorithm for quantum computers. Period finding is the key part of the algorithm, which is accomplished with the help of quantum superposition of states and quantum entanglement. The period finding can be also accomplished using classical wave superposition. In this study, we present experimental data obtained on a multi-port spin wave interferometer made of Y3Fe2(FeO4)3. Number 817 was factorized by a sequence of phase measurements. We also present the results of numerical modeling on the prime factorization of larger numbers 334 597 , 1 172 693 , 3 377 663 , and 9 363 239. The results of numerical modeling reveal significant shortcomings of the period-based approach. The major problems are associated with an inability to predict the period of the modular function, significant overhead over classical digital computers in some cases, and phase accuracy requirements. We argue that the same problems are inherent in classical analog and quantum computers. [ABSTRACT FROM AUTHOR]

We describe solutions of asymptotically AdS3 Einstein gravity that are sourced by the insertion of operators in the boundary CFT2, whose dimension scales with the central charge of the theory. Previously, we found that the geometry corresponding to a black hole two-point function is simply related to an infinite covering of the Euclidean BTZ black hole [1]. However, here we find that the geometry sourced by the presence of a third black hole operator turns out to be a Euclidean wormhole with two asymptotic boundaries. We construct this new geometry as a quotient of empty AdS3 realized by domes and doors. The doors give access to the infinite covers that are needed to describe the insertion of the operators, while the domes describe the fundamental domains of the quotient on each cover. In particular, despite the standard fact that the Fefferman-Graham expansion is single-sided, the extended bulk geometry contains a wormhole that connects two asymptotic boundaries. We observe that the two-sided wormhole can be made single-sided by cutting off the wormhole and gluing on a "Lorentzian cap". In this way, the geometry gives the holographic description of a three-point function, up to phases. By rewriting the metric in terms of a Liouville field, we compute the on-shell action and find that the result matches with the Heavy-Heavy-Heavy three-point function predicted by the modular bootstrap. Finally, we describe the geometric transition between doors and defects, that is, when one or more dual operators describe a conical defect insertion, rather than a black hole insertion. [ABSTRACT FROM AUTHOR]

We consider a two-stage submodular maximization problem subject to a cardinality constraint and k matroid constraints, where the objective function is the expected difference of a nonnegative monotone submodular function and a nonnegative monotone modular function. We give two bi-factor approximation algorithms for this problem. The first is a deterministic $\left({{1 \over {k + 1}}\left({1 - {1 \over {{e^{k + 1}}}}} \right),1} \right)$ -approximation algorithm, and the second is a randomized $\left({{1 \over {k + 1}}\left({1 - {1 \over {{e^{k + 1}}}}} \right) - \varepsilon ,1} \right)$ -approximation algorithm with improved time efficiency. [ABSTRACT FROM AUTHOR]

We study Apollonian circle packings using the properties of a certain rank 4 indefinite Kac-Moody root system \Phi. We introduce the generating function Z(\mathbf {s}) of a packing, an exponential series in four variables with an Apollonian symmetry group, which is a symmetric function for \Phi. By exploiting the presence of affine and Lorentzian hyperbolic root subsystems of \Phi, with automorphic Weyl denominators, we express Z(\mathbf {s}) in terms of Jacobi theta functions and the Siegel modular form \Delta _5. We also show that the domain of convergence of Z(\mathbf {s}) is the Tits cone of \Phi, and discover that this domain inherits the intricate geometric structure of Apollonian packings. [ABSTRACT FROM AUTHOR]

In 2021 da Silva, Hirschhorn, and Sellers studied a wide variety of congruences for the k -elongated plane partition function d k (n) by various primes. They also conjectured the existence of an infinite congruence family modulo arbitrarily high powers of 2 for the function d 7 (n). We prove that such a congruence family exists — indeed, for powers of 8. The proof utilizes only classical methods, i.e. integer polynomial manipulations in a single function, in contrast to all other known infinite congruence families for d k (n) which require more modern methods to prove. [ABSTRACT FROM AUTHOR]

We prove Rogers–Ramanujan-type identities for the Nahm sums associated with the tadpole Cartan matrix of rank 3. These identities reveal the modularity of these sums, and thereby we confirm a conjecture of Calinescu, Penn and the first author in this case. We show that these Nahm sums together with some shifted sums can be combined into a vector-valued modular function on the full modular group. We also present some conjectures for a general rank. [ABSTRACT FROM AUTHOR]

Objective Scatter Index (OSI) and the Modular Transfer Function (MTF) by HD Analyzer®. Two QoV questionnaires were applied to patients in which both eyes were included: the McAlinden and the Catquest-9 SF. Results: We included 50 eyes (28 patients). The mean follow-up time was 5.4± 1.0 years. Comparing to month 1 after surgery, at the last follow-up visit, there was a decrease in the uncorrected visual acuity (0.14± 0.13 vs 0.08± 0.09 LogMAR, p=0.024), a negative increase in the spherical equivalent (− 0.31± 0.60 vs − 0.02± 0.20, p=0.006) and no changes in the best-corrected visual acuity (p> 0.999). An uncorrected near visual acuity of at least J2 was achieved in 89% of eyes one month after surgery and in 91% of eyes at the last follow-up visit (p=0.829). At the last follow-up, the mean OSI was 5.1± 1.8 and the mean MTF was 17.5± 10.6. Some degree of near vision difficulty was reported by 91% of patients, and 74% of patients reported photic phenomena (halos, glare, starbursts). However, most patients reported that these symptoms caused none to little bothersome. At the last follow-up, 87% of patients were at least fairly satisfied with the surgery. Conclusion: Even after a mean follow-up time of 5 years, patients maintained good uncorrected visual acuity. Even though most patients experienced some degree of near vision difficulty and visual symptoms, globally, our patients were satisfied with their current vision, and the experienced symptoms did not have a significant impact on their daily lives. [ABSTRACT FROM AUTHOR]

Featured Application: TraumaMeter v.873 was designed to increase the accuracy of specific measurements at the spine level. The system meets the characteristics of open-source and modular functions and has been extended to perform angular measurements on lower extremity X-ray studies with high reliability. To establish classifications and to obtain pre- and post-operative information on patient-specific alignments, it is necessary to measure different angular values accurately and precisely, mainly on weight-bearing, full-length anteroposterior X-rays of the lower limbs (LLRs). This study evaluated angular measurements' validity and absolute reliability on LLRs with a self-developed, computer-aided measurement system (TraumaMeter v.873). Eight independent observers measured the preoperative mechanical hip-knee-ankle (mHKA) angle of 52 lower extremities (26 cases) in a blinded fashion on three occasions separated by two weeks. We obtained an intra-observer mean bias error (MBE) of 0.40°, a standard deviation (SD) of 0.11°, and a 95% confidence interval (CI) of 0.37°–0.43°. We also obtained an inter-observer MBE of 0.49°, an SD of 0.15°, and a 95% C of 0.45°–0.53°. The intra-observer MBE for the measurement pair between the second and the first measurement round (T2T1) was 0.43°, the SD was 0.13°, and the 95% CI was 0.39°–0.47°; the MBE between the third and the second round (T3T2) was 0.37°, with an SD of 0.10° and a 95% CI of 0.34°–0.40°; and the MBE between the third and the first round (T3T1) was 0.40°, with an SD of 0.10° and a 95% CI of 0.37°–0.43°. The interobserver MBE for the first round of measurements was 0.52°, with an SD of 0.16° and a 95% CI of 0.48°–0.56°; the MBE for the second round was 0.50°, with an SD of 0.15° and a 95% CI of 0.46°–0.54°; and the MBE for the third round was 0.46°, with an SD of 0.14° and a 95% CI of 0.42°–0.50°. There were no statistically significant differences in the inter-observer errors for the three tests. In the case of the intra-observer analysis, there were differences between T2T1 and between T3T2, but these differences were minimal, with no overlaps in the lower or upper values, respectively, of the confidence intervals. These results led us to conclude that the TraumaMeter v.873 software extension for measuring lower-limb angles in LLRs is an accurate tool with low intra- and inter-observer variability. [ABSTRACT FROM AUTHOR]

Viazovska's solution of the sphere packing problem in eight dimensions is based on a remarkable construction of certain special functions using modular forms. Great mathematics has consequences far beyond the problems that originally inspired it, and Viazovska's work is no exception. In this article, we'll examine how it has led to new interpolation theorems in Fourier analysis, specifically a theorem of Radchenko and Viazovska. [ABSTRACT FROM AUTHOR]

Simple Summary: The health of Amphioctopus fangsiao, a species used in aquaculture or fish farming, can be greatly affected by infections. To understand how their immune system responds, we looked at the changes in their immune cells when exposed to substances that mimic these infections. By studying these responses, we were able to identify key parts of their immune system that change when faced with infection-causing threats. We also discovered important genes, including PKMYT1 (protein kinase, membrane associated tyrosine/threonine 1) and NAMPT (nicotinamide phosphoribosyltransferase), that play a crucial role in this response. Our study gives us a deeper understanding of the immune system of the Amphioctopus fangsiao. The primary influencer of aquaculture quality in Amphioctopus fangsiao is pathogen infection. Both lipopolysaccharides (LPS) and polyinosinic:polycytidylic acid (Poly I:C) are recognized by the pattern recognition receptor (PRR) within immune cells, a system that frequently serves to emulate pathogen invasion. Hemolymph, which functions as a transport mechanism for immune cells, offers vital transcriptome information when A. fangsiao is exposed to pathogens, thereby contributing to our comprehension of the species' immune biological mechanisms. In this study, we conducted analyses of transcript profiles under the influence of LPS and Poly I:C within a 24 h period. Concurrently, we developed a Weighted Gene Co-expression Network Analysis (WGCNA) to identify key modules and genes. Further, we carried out Gene Ontology (GO) and Kyoto Encyclopedia of Genes and Genomes (KEGG) enrichment analyses to investigate the primary modular functions. Co-expression network analyses unveiled a series of immune response processes following pathogen stress, identifying several key modules and hub genes, including PKMYT1 and NAMPT. The invaluable genetic resources provided by our results aid our understanding of the immune response in A. fangsiao hemolymph and will further our exploration of the molecular mechanisms of pathogen infection in mollusks. [ABSTRACT FROM AUTHOR]

There is a relation between hypergeometric function and conformal mapping. Based on this relationship, we study the map ... which is associated with the generalized modular equation ... in the Ramanujan's theories of signatures 1 s = 2, 3, and 4. It is proved that the inverse mapping ρ of ζ can be analytically extended as a single-valued function on the upper half-plane H only for 1 s = 2, 3, and 4. For the triangle group ... associated with the generalized modular equation, we also investigate various properties of the mapping f : H → G\H which constructs an infinite cover of the thrice punctured Riemann sphere C \ {0, 1,∞}. [ABSTRACT FROM AUTHOR]

In this work we start from near vector spaces, which we endow with some additional properties that allow convex analysis. The seminormed structure used here will also be improved by adding properties such as the null condition and null equality, thus resulting in a new type of space, which is still weaker than the conventional Banach structures: pre-convex regular near-Banach space. On the newly defined structure, we introduce the concept of uniform convexity and analyze several resulting properties. The major outcomes prove a remarkable resemblance to the classical properties resulting from uniform convexity on hyperbolic metric spaces or modular function spaces, including the famous Browder-Gohde fixed point theorem. [ABSTRACT FROM AUTHOR]

This article discusses the scientific publication rate in research on disorders of consciousness (DoC). The authors note that there has been an increase in publications on the topic, particularly in the use of neuroimaging techniques such as fMRI, PET scans, and EEG studies. However, they also observe a decrease in publication rates since 2013-2015. The authors suggest that this decline may be due to various factors, including limitations in data interpretation and the cost-benefit ratio of advanced technologies. They emphasize the need for further research and the application of advanced technologies in understanding consciousness. [Extracted from the article]

Motivation 3D chromatin structure plays an important role in regulating gene expression and alterations to this structure can result in developmental abnormalities and disease. While genomic approaches like Hi-C and Micro-C can provide valuable insights in 3D chromatin architecture, the resulting datasets are extremely large and difficult to manipulate. Results Here, we present mariner , a rapid and memory efficient tool to extract, aggregate, and plot data from Hi-C matrices within the R/Bioconductor environment. Mariner simplifies the process of querying and extracting contacts from multiple Hi-C files using a parallel and block-processing approach. Modular functions allow complete workflow customization for advanced users, yet all-in-one functions are available for running the most common types of analyses. Finally, tight integration with existing Bioconductor infrastructure enables complete analysis and visualization of Hi-C data in R. Availability and implementation Available on GitHub at https://github.com/EricSDavis/mariner and on Bioconductor at https://www.bioconductor.org/packages/release/bioc/html/mariner.html. [ABSTRACT FROM AUTHOR]

Let p be a prime number. Continuing and extending our previous paper with the same title, we prove explicit rates of overconvergence for modular functions of the form E k ∗ V (E k ∗) where E k ∗ is a classical, normalized Eisenstein series on Γ 0 (p) and V the p-adic Frobenius operator. In particular, we extend our previous paper to the primes 2 and 3. For these primes our main theorem improves somewhat upon earlier results by Emerton, Buzzard and Kilford, and Roe. We include a detailed discussion of those earlier results as seen from our perspective. We also give some improvements to our earlier paper for primes p ≥ 5 . Apart from establishing these improvements, our main purpose here is also to show that all of these results can be obtained by a uniform method, i.e., a method where the main points in the argumentation is the same for all primes. We illustrate the results by some numerical examples. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the concept of triangular ideal relative convergence for double sequences of functions defined on a modular space. Based upon this new convergence method, we prove Korovkin theorems. Then, we construct an example such that our new approximation results work. Finally, we discuss the reduced results which are obtained by special choices. [ABSTRACT FROM AUTHOR]

We investigate the existence of solutions for the Fredholm integral equation Φ (ϑ) = G (ϑ , Φ (ϑ)) + ∫ 0 1 F (ϑ , ζ , Φ (ζ)) d ζ , for ϑ ∈ [ 0 , 1 ] , in the setting of the modular function spaces L ρ . We also derive an application of this research within the framework of variable exponent Lebesgue spaces L p (·) subject to specific conditions imposed on the exponent function p (·) and the functions F and G. [ABSTRACT FROM AUTHOR]

We prove the modular convexity of the mixed norm L p (ℓ 2) on the Sobolev space W 1 , p (Ω) in a domain Ω ⊂ R n under the sole assumption that the exponent p (x) is bounded away from 1, i.e., we include the case sup x ∈ Ω p (x) = ∞ . In particular, the mixed Sobolev norm is uniformly convex if 1 < inf x ∈ Ω p (x) ≤ sup x ∈ Ω p (x) < ∞ and W 0 1 , p (Ω) is uniformly convex. [ABSTRACT FROM AUTHOR]

Generalised Eisenstein series are non-holomorphic modular invariant functions of a complex variable, τ, subject to a particular inhomogeneous Laplace eigenvalue equation on the hyperbolic upper-half τ-plane. Two infinite classes of such functions arise quite naturally within different string theory contexts. A first class can be found by studying the coefficients of the effective action for the low-energy expansion of type IIB superstring theory, and relatedly in the analysis of certain integrated four-point functions of stress tensor multiplet operators in N = 4 supersymmetric Yang-Mills theory. A second class of such objects is known to contain all two-loop modular graph functions, which are fundamental building blocks in the low-energy expansion of closed-string scattering amplitudes at genus one. In this work, we present a Poincaré series approach that unifies both classes of generalised Eisenstein series and manifests certain algebraic and differential relations amongst them. We then combine this technique with spectral methods for automorphic forms to find general and non-perturbative expansions at the cusp τ → i∞. Finally, we find intriguing connections between the asymptotic expansion of these modular functions as τ → 0 and the non-trivial zeros of the Riemann zeta function. [ABSTRACT FROM AUTHOR]