Search

For each of (i) arbitrary stochastic reset, (ii) deterministic reset with arbitrary period, (iii) reset at arbitrary constant rate, and then in the sense of either (a) first-order stochastic dominance or (b) expectation (i.e. for each of the six possible combinations of the preceding), those laws of random times are precisely characterized that are rendered no bigger [rendered no smaller; left invariant] by all possible restart laws (within the classes (i), (ii), (iii), as the case may be). Partial results in the same vein for reset with branching are obtained. In particular it is found that deterministic and arbitrary stochastic restart lead to the same characterizations, but this equivalence fails to persist for exponential (constant-rate) reset.

Describing systems in terms of choices and their resulting costs and rewards offers the promise of freeing algorithm designers and programmers from specifying how those choices should be made; in implementations, the choices can be realized by optimization techniques and, increasingly, by machine-learning methods. We study this approach from a programming-language perspective. We define two small languages that support decision-making abstractions: one with choices and rewards, and the other additionally with probabilities. We give both operational and denotational semantics. In the case of the second language we consider three denotational semantics, with varying degrees of correlation between possible program values and expected rewards. The operational semantics combine the usual semantics of standard constructs with optimization over spaces of possible execution strategies. The denotational semantics, which are compositional, rely on the selection monad, to handle choice, augmented with an auxiliary monad to handle other effects, such as rewards or probability. We establish adequacy theorems that the two semantics coincide in all cases. We also prove full abstraction at base types, with varying notions of observation in the probabilistic case corresponding to the various degrees of correlation. We present axioms for choice combined with rewards and probability, establishing completeness at base types for the case of rewards without probability.

Large-scale complex network data poses significant challenges for the analytic ideas and tools to monitor and analyze complex networks. As classical structure descriptors, average path length ( $L$ ), global and local network efficiency ( $E_{glob}$ and $E_{loc}$ ), general and loop clustering coefficient ( $C_{3}$ and $D$ ), play significant roles in complex network analysis. In this paper, we make use of resistive distance instead of the shortest path distance to suggest resistive distance descriptors, i.e., $L_{r}$ , $\Omega _{glob}$ and $\Omega _{loc}$ , $\Omega _{3}$ and $D_{r}$ . We investigate all the resistive descriptors on classical WS, BA and ER models and find some interesting phenomenons. On one hand, $L_{r}$ and $\Omega _{3}$ (resp., $\Omega _{glob}$ and $\Omega _{loc}$ ) can be used to characterize the features of small-word networks. On the other hand, $L_{r}$ , $\Omega _{3}$ , and $\Omega _{glob}$ can be utilized to measure network invulnerability. To access the effectiveness of the resistive distance descriptors, we conduct extensive numerical simulations on synthetic and real networks. In comparison with the baselines, the proposed metrics show competitive performance on classical network models and are more efficient for networks with small and medium size.

An ultra-low specific on-resistance 4H-SiC power laterally diffused metal oxide semiconductor (LDMOS) device is proposed for 1200V-class applications. In the proposed SiC LDMOS device, a double-trench gate is introduced to reduce the channel region resistance. And a p-type variation lateral doping (VLD) region is also employed in the drift region, which not only optimizes the surface electric field and improves the breakdown voltage, but also increases the doping concentration of the N-drift region, resulting in a low drift region resistance. So that, the proposed device achieves an ultra-low specific on-resistance ( ${R} _{\mathrm{ on,sp}}$ ). Numerical Simulation results show that the ${R} _{\mathrm{ on,sp}}$ of the proposed SiC LDMOS is 3.5 $\text{m}\boldsymbol{\Omega }\cdot {\mathrm{ cm}}^{2}$ with a breakdown voltage of ~1460V, which is reduced by more than 46% compared with the conventional field-plate SiC LDMOS with a ${R} _{\mathrm{ on,sp}}$ of 6.6 $\text{m}\boldsymbol{\Omega }\cdot {\mathrm{ cm}}^{2}$ and a breakdown voltage of ~1210V. The transconductance of the proposed device is improved greatly. And the trade-off relationship between the ${R} _{\mathrm{ on,sp}}$ and the breakdown voltage is also significantly improved compared with those of the conventional device and the previous literature.

A $(m,n)$ sonar sequence is an $m\times n$ array with exactly one dot in each column and where all lines connecting two dots in the array are distinct as vectors. These arrays are known to have many applications such as sonar and radar detection and these are studied as a particular case of Golomb rectangles or two-dimensional Sidon sets. The main open problem for sonar sequences is: for fixed $m$ , find the largest $n$ for which there is an $(m,n)$ sonar sequence, these sequences are called the best sonar sequences. The extended sonar sequences are generalizations of sonar sequences where each column has at most one dot, the motivation to study these arrays are the best results obtained when applied to radar and sonar detection. In this paper, we give the best sonar sequences with $m\leq 100$ obtained from an exhaustive computational search based on the Caicedo, Ruiz and Trujillo constructions and we present new constructions of extended sonar sequences that use Sidon sets.

In this paper, our aim is to obtain the $ K_2 $ analogues of both the Herbrand-Ribet theorem and the Vandiver's conjecture.

In this paper, we consider the performance of exclusive-OR (XOR) rule in detecting the presence or absence of a deterministic signal in bivariate Gaussian noise. Signals, when present at the two sensors, are assumed unequal, whereas the noise components have identical marginal distribution but are correlated. The sensors send their one-bit quantized data to a fusion center, which then employs the XOR rule to arrive at the final decision. Here we prove that, in the limit as the correlation coefficient $r$ approaches 1, the optimum fusion rule for both parallel and tandem topologies is XOR with identical, alternating partitions (XORAP) of the observations at the sensors. We further quantify the asymptotic decrease of the Bayes error of XORAP towards zero as a constant multiplied by $\sqrt {1-r}$ , as $r$ approaches 1. When compared to the asymptotic Bayes error of CLRT, which decreases to zero exponentially fast, as a function of $1/(1-r)$ , the Bayes error of XORAP decreases to zero much slower.

In this paper, we present a Model-Free Stochastic Inverse Optimal Control (IOC) algorithm for the discrete-time infinite-horizon stochastic linear quadratic regulator (LQR). Our proposed algorithm exploits the richness of the available system trajectories to recover the control gain $K$ and cost function parameters $(Q,R)$ in a low (space, sample, and computational) complexity manner. By leveraging insights on the stochastic LQR, we guarantee well-posedness of the Model-Free Stochastic IOC LQR via satisfaction of the Certainty Equivalence optimality conditions. The exact solution of the control gain $K$ is recovered via a deterministic, low complexity Least Squares approach. Using $K$ , we solve a completely model-free non-iterative SemiDefinite Programming (SDP) problem to obtain a unique (up to a scalar ambiguity) $(Q,R)$ , in which optimality and feasibility are jointly ensured. Via derivation of the sample complexity bounds, we show that the non-asymptotic performance of the Model-Free Stochastic IOC LQR can be characterized by the signal-to-noise (SNR) ratio of the finite set of system state and input signals. We present a model-based version of the algorithm for the special case where $(A,B)$ is available, and we, further, provide the extension to the Stochastic Model-Free IOC linear quadratic tracking (LQT) case.

Sea ice concentration algorithms using brightness temperatures ($T_{B}$) from satellite microwave radiometers are used to compute sea ice concentration ($c_{\text{ice}}$), sea ice extent, and generate sea ice climate data records. Therefore, it is important to minimize the sensitivity of $c_{\text{ice}}$ estimates to geophysical noise caused by snow/sea ice thermal microwave emission signature variations, and presence of WV and clouds in the atmosphere and/or near-surface winds. In this study, we investigate the effect of geophysical noise leading to systematic $c_{\text{ice}}$ biases and affecting $c_{\text{ice}}$ standard deviations (STD) using simulated top of the atmosphere $T_{B}$s over open water and 100% sea ice. We consider three case studies for the Arctic and the Antarctic and eight different $c_{\text{ice}}$ algorithms, representing different families of algorithms based on the selection of channels and methodologies. Our simulations show that, over open water and low $c_{\text{ice}}$, algorithms using gradients between V-polarized 19-GHz and 37-GHz $T_{B}$s show the lowest sensitivity to the geophysical noise, while the algorithms exclusively using near-90-GHz channels have by far the highest sensitivity. Over sea ice, the atmosphere plays a much smaller role than over open water, and the $c_{\text{ice}}$ STD for all algorithms is smaller than over open water. The hybrid and low-frequency (6 GHz) algorithms have the lowest sensitivity to noise over sea ice, while the polarization type of algorithms has the highest noise levels.

$(\alpha,\beta)$ -Pythagorean fuzzy set is a very efficient way of dealing with uncertainty. In this article, we have introduced the notions of $(\alpha,\beta)$ - Pythagorean fuzzy subring and $(\alpha,\beta)$ - Pythagorean fuzzy ideal of a ring. Further, we have briefly described various results related to it. Also, we have discussed the level subring of an $(\alpha,\beta)$ - Pythagorean fuzzy subring. Moreover, we have studied the direct product and ring homomorphism of $(\alpha,\beta)$ - Pythagorean fuzzy subrings.

A hybrid multi-state orbital angular momentum-multi pulse-position modulation ( $N$ OAM-MPPM) scheme over gamma-gamma free-space optical ( ${\Gamma \Gamma }$ -FSO) channel is studied in this paper. In our study, all atmospheric and pointing error impacts are taken into account. Expressions for the parameters of ${\Gamma \Gamma }$ -FSO-pointing error channel are derived. In addition, approximate-tight upper bounds on the bit-error rates (BERs) of $N$ OAM and $N$ OAM-MPPM techniques are developed over ${\Gamma \Gamma }$ -FSO-pointing error channels, considering the influences of beam divergence and pointing error (PE). The ${\Gamma \Gamma }$ -FSO-PE channel parameters and the BER expressions are evaluated numerically and verified by simulation. It turned out that the analytical results are nearly the same as those obtained from simulation under different turbulence scenarios and OAM modes. The results demonstrate that under variable turbulence conditions, the $N$ OAM-MPPM technique outperforms both ordinary $N$ OAM and MPPM systems. Furthermore, different deep learning (DL) techniques, namely random forest (RF), convolution neural network (CNN), and auto-encoder (AE), are employed to get the optimum classification accuracy using different datasets of $N$ OAM-MPPM over ${\Gamma \Gamma }$ -PE channel model. Finally, the results indicate that AE has the best performance metrics compared to other models using different datasets.

We propose a ring-core photonic quasi-crystal fiber (RC-PQCF) featuring a ring-shaped fiber core and two symmetrical SiO2 stress-applying parts (SAPs). By optimizing the mole percentage of GeO2 and geometrical parameters of the fiber, the design supports 34 full vector polarization modes (FV-PMs). The effective refractive index difference ($\Delta {n_{eff}}$) of adjacent FV-PMs is larger than $1.07 \times {10^{ - 4}}$ at 1550 nm. The confinement loss (${\mathrm{\alpha }}$) of FV-PMs is less than ${10^{ - 6}}$, which is sufficient to confine the light field in the ring-core. Through numerical analysis, broadband performance is investigated subsequently in the 1500–1600 nm. The dispersion (${D_\lambda }$) of FV-PMs is less than $138.14{\mathrm{\ ps}} \cdot {\mathrm{n}}{{\mathrm{m}}^{ - 1}} \cdot {\mathrm{k}}{{\mathrm{m}}^{ - 1}}$ and maintains a flat trend. The mode field area (${A_{eff}}$) of FV-PMs is larger compared to single mode fibers and the nonlinear coefficient (${\mathrm{\gamma }}$) of FV-PMs is within ($6.97 \times {10^{ - 4}}$, $1.54 \times {10^{ - 3}}$) ${{\mathrm{m}}^{ - 1}} \cdot {{\mathrm{W}}^{ - 1}}{\mathrm{\ }}$ in the 1500–1600 nm. The fiber is a promising design for mode division multiplexing (MDM) that supports the MIMO-free processing and improves the transmission capacity and spectral efficiency.

A category theory constitutes a convenient conceptual apparatus to organize the worlds of mathematical entities. The concept of fuzzy natural transformation as an abstract mapping on functors is one of the essential concepts of this theory. If we admit a piece of non-commutativity in its definition diagrams, then the ‘upward’ and the ‘downward’ diagram parts generate different result sets. In this way, we can introduce the concept of fuzzy natural transformation. We deal with the multi-fuzzy natural transformation if such a transformation is based on a multi-diagram. This paper aims to describe the multi-fuzzy natural transformation situation when the symmetric difference of the result is finite. It allows us to organize the whole spectrum of the result sets in a unique quotient algebra $\mathcal {P}^{comp}(\omega)/\mathrm {fin}$ . Different algebraic properties of this structure will be explored, and a piece of classical encoding theory will be reconstructed in the environment determined by this algebra. In particular, the concepts of the $k$ -multi similarity, the abstract $k$ -multi similarity, the $k$ -similarity balls, and the abstract $k$ -similarity balls are introduced as some generalization of the idea of Hamming’s distances and Hamming’s balls. Finally, it is shown how to automate some verification processes in this context using an R-based programming environment.

We introduce Concurrent NetKAT (CNetKAT), an extension of NetKAT with operators for specifying and reasoning about concurrency in scenarios where multiple packets interact through state. We provide a model of the language based on partially-ordered multisets (pomsets), which are a well-established mathematical structure for defining the denotational semantics of concurrent languages. We provide a sound and complete axiomatization of this model, and we illustrate the use of CNetKAT through examples. More generally, CNetKAT can be understood as an algebraic framework for reasoning about programs with both local state (in packets) and global state (in a global store).

We develop a constructive theory of finite multisets in Homotopy Type Theory, defining them as free commutative monoids. After recalling basic structural properties of the free commutative-monoid construction, we formalise and establish the categorical universal property of two, necessarily equivalent, algebraic presentations of free commutative monoids using 1-HITs. These presentations correspond to two different equational theories invariably including commutation axioms. In this setting, we prove important structural combinatorial properties of finite multisets. These properties are established in full generality without assuming decidable equality on the carrier set. As an application, we present a constructive formalisation of the relational model of classical linear logic and its differential structure. This leads to constructively establishing that free commutative monoids are conical refinement monoids. Thereon we obtain a characterisation of the equality type of finite multisets and a new presentation of the free commutative-monoid construction as a set-quotient of the list construction. These developments crucially rely on the commutation relation of creation/annihilation operators associated with the free commutative-monoid construction seen as a combinatorial Fock space., Comment: Appeared in MFPS'22

An F-system is a computational model that performs a folding operation on words of a given language, following directions coded on words of another given language. This paper considers the case in which both given languages are regular, and it shows that the class of languages generated by such F-systems is a proper subset of the class of linear context-free languages., Comment: Nine pages. This is the accepted version of a manuscript submitted for publication in Information Processing Letters

Knaster-Tarski’s theorem, characterising the greatest fix- point of a monotone function over a complete lattice as the largest post-fixpoint, naturally leads to the so-called coinduction proof principle for showing that some element is below the greatest fixpoint (e.g., for providing bisimilarity witnesses). The dual principle, used for showing that an element is above the least fixpoint, is related to inductive invariants. In this paper we provide proof rules which are similar in spirit but for showing that an element is above the greatest fixpoint or, dually, below the least fixpoint. The theory is developed for non-expansive monotone functions on suitable lattices of the form$$\mathbb {M}^Y$$MY, whereYis a finite set and$$\mathbb {M}$$Man MV-algebra, and it is based on the construction of (finitary) approximations of the original functions. We show that our theory applies to a wide range of examples, including termination probabilities, behavioural distances for probabilistic automata and bisimilarity. Moreover it allows us to determine original algorithms for solving simple stochastic games.

The paper presents a new approach to autotuning data-parallel programs. Autotuning is a search for optimal program settings which maximize its performance. The novelty of the approach lies in the use of the model checking method to find the optimal tuning parameters by the method of counterexamples. In our work, we abstract from specific programs and specific processors by defining their representative abstract patterns. Our method of counterexamples implements the following four steps. At the first step, an execution model of an abstract program on an abstract processor is described in the language of a model checking tool. At the second step, in the language of the model checking tool, we formulate the optimality property that depends on the constructed model. At the third step, we find the optimal values of the tuning parameters by using a counterexample constructed during the verification of the optimality property. In the fourth step, we extract the information about the tuning parameters from the counter-example for the optimal parameters. We apply this approach to autotuning parallel programs written in OpenCL, a popular modern language that extends the C language for programming both standard multi-core processors (CPUs) and massively parallel graphics processing units (GPUs). As a verification tool, we use the SPIN verifier and its model representation language Promela, whose formal semantics is good for modelling the execution of parallel programs on processors with different architectures.

Hadronic resonances play an important role in the study of the physics of heavy-ion collisions. In these proceedings, we discuss how the resonances can probe the reaction dynamics, the strangeness production and the properties of the hadronic phase in heavy-ion collisions at center-of-mass energies of sNN = 4–11 GeV. The resonance properties predicted by the general-purpose event generators are found to be very sensitive to the properties and space-time evolution of the medium produced in heavy-ion collisions.

The paper presents a new mathematical model of parallel programs, on the basis of which it is possible, in particular, to verify parallel programs presented on a certain subset of the parallel programming interface MPI. This model is based on the concepts of a sequential and distributed process. A parallel program is modeled as a distributed process in which sequential processes communicate by asynchronously sending and receiving messages over channels. The main advantage of the described model is the ability to simulate and verify parallel programs that generate an indefinite number of sequential processes. The proposed model is illustrated by the application of verification of the matrix multiplication MPI program.

Using OI6300 airglow images collected over São João do Cariri (7.4∘ S, 36.5∘ W) from 2000 to 2007, the equatorial plasma bubble (EPB) zonal drifts were calculated. A strong day-to-day variability was observed in the EPB zonal drifts, which is directly associated with the very complex dynamics of the nighttime thermosphere–ionosphere system near the Equator. The present work investigated the contribution of the semidiurnal lunar tide M2 for the EPB zonal drifts. The M2 presented an amplitude of 3.1 m s−1 in the EPB zonal drifts, which corresponds to 5.6 % of the average drifts. The results showed that the M2 amplitudes in the EPB zonal drifts were solar cycle and seasonally dependent. The amplitude of the M2 was stronger during the high solar activity, reaching over 10 % of the EPB zonal drift average. Regarding the seasons, during the Southern Hemisphere summer, the M2 amplitude was twice as large (12 %) compared to the equinox ones. The seasonality agrees with other observations of the M2 in the ionospheric parameters such as vertical drifts and electron concentration, for instance. On the other hand, the very large M2 amplitudes found during the high solar activity agree with previous observations of the lunar tide in the ionospheric E region.

The purpose of this study is to introduce the new class of Hermite–Hadamard inequality for LR-convex interval-valued functions known as LR-interval Hermite–Hadamard inequality, by means of pseudo-order relation ( ≤p ). This order relation is defined on interval space. We have proved that if the interval-valued function is LR-convex then the inclusion relation “ ⊆ ” coincident to pseudo-order relation “ ≤p ” under some suitable conditions. Moreover, the interval Hermite–Hadamard–Fejér inequality is also derived for LR-convex interval-valued functions. These inequalities also generalize some new and known results. Useful examples that verify the applicability of the theory developed in this study are presented. The concepts and techniques of this paper may be a starting point for further research in this area.

In this paper, algebraic relations were established that determined the invariance of a transformed number after several transformations. The restrictions that determine the group structure of these relationships were analyzed, as was the case of the Klein group. Parametric Kr functions associated with the existence of cycles were presented, as well as the role of the number of their links in the grouping of numbers in higher-order equivalence classes. For this, we developed a methodology based on binary equivalence relations and the complete parameterization of the Kaprekar routine using Ki functions of parametric transformation.

This paper addresses an H2 optimal control problem for a class of discrete-time stochastic systems with Markov jump parameter and multiplicative noises. The involved Markov jump parameter is a uniform ergodic Markov chain taking values in a Borel-measurable set. In the presence of exogenous white noise disturbance, Gramian characterization is derived for the H2 norm, which quantifies the stationary variance of output response for the considered systems. Moreover, under the condition that full information of the system state is accessible to measurement, an H2 dynamic optimal control problem is shown to be solved by a zero-order stabilizing feedback controller, which can be represented in terms of the stabilizing solution to a set of coupled stochastic algebraic Riccati equations. Finally, an iterative algorithm is provided to get the approximate solution of the obtained Riccati equations, and a numerical example illustrates the effectiveness of the proposed algorithm.

The family of cumulative paired ϕ-entropies offers a wide variety of ordinal dispersion measures, covering many well-known dispersion measures as a special case. After a comprehensive analysis of this family of entropies, we consider the corresponding sample versions and derive their asymptotic distributions for stationary ordinal time series data. Based on an investigation of their asymptotic bias, we propose a family of signed serial dependence measures, which can be understood as weighted types of Cohen’s κ, with the weights being related to the actual choice of ϕ. Again, the asymptotic distribution of the corresponding sample κϕ is derived and applied to test for serial dependence in ordinal time series. Using numerical computations and simulations, the practical relevance of the dispersion and dependence measures is investigated. We conclude with an environmental data example, where the novel ϕ-entropy-related measures are applied to an ordinal time series on the daily level of air quality.

In this paper, the author considers twisted q-analogues of Catalan-Daehee numbers and polynomials by using p-adic q-integral on Zp. We derive some explicit identities for those twisted numbers and polynomials related to various special numbers and polynomials.

For random walks on a complex network, the configuration of a network that provides optimal or suboptimal navigation efficiency is meaningful research. It has been proven that a complete graph has the exact minimal mean hitting time, which grows linearly with the network order. In this paper, we present a class of sparse networks G(t) in view of a graphic operation, which have a similar dynamic process with the complete graph; however, their topological properties are different. We capture that G(t) has a remarkable scale-free nature that exists in most real networks and give the recursive relations of several related matrices for the studied network. According to the connections between random walks and electrical networks, three types of graph invariants are calculated, including regular Kirchhoff index, M-Kirchhoff index and A-Kirchhoff index. We derive the closed-form solutions for the mean hitting time of G(t), and our results show that the dominant scaling of which exhibits the same behavior as that of a complete graph. The result could be considered when designing networks with high navigation efficiency.

In this paper, we develop some Hermite–Hadamard–Fejér type inequalities for n-times differentiable functions whose absolute values of n-th derivatives are (α,m)-convex function. The results obtained in this paper are extensions and generalizations of the existing ones. As a special case, the generalization of the remainder term of the midpoint and trapezoidal quadrature formulas are obtained.

Among various modifications of the permutation entropy defined as the Shannon entropy of the ordinal pattern distribution underlying a system, a variant based on Rényi entropies was considered in a few papers. This paper discusses the relatively new concept of Rényi permutation entropies in dependence of non-negative real number q parameterizing the family of Rényi entropies and providing the Shannon entropy for q=1. Its relationship to Kolmogorov–Sinai entropy and, for q=2, to the recently introduced symbolic correlation integral are touched.

Swirling has a significant effect on the main characteristics of flow and can lead to its fundamental restructuring. On the flow axis, a stagnation point with zero velocity is possible, behind which a return flow zone is formed. The apparent instability leads to the formation of secondary vortex motions and can also be the cause of vortex breakdown. In the paper, a swirling flow with a velocity profile of the Batchelor vortex type has been studied on the basis of the linear hydrodynamic stability theory. An effective numerical method for solving the spectral problem has been developed. This method includes the asymptotic solutions at artificial and irregular singular points. The stability of flows was considered for the values of the Reynolds number in the range 10≤Re≤5×106. The calculations were carried out for the value of the azimuthal wavenumber parameter n=−1. As a result of the analysis of the solutions, the existence of up to eight simultaneously occurring unstable modes has been shown. The paper presents a classification of the detected modes. The critical parameters are calculated for each mode. For fixed values of the Reynolds numbers 60≤Re≤5000, the curves of neutral stability are plotted. Branching points of unstable modes are found. The maximum growth rates for each mode are determined. A new viscous instability mode is found. The performed calculations reveal the instability of the Batchelor vortex at large values of the swirl parameter for long-wave disturbances.

The gas transfer velocity (k) is a major source of uncertainty when assessing the magnitude of lake gas exchange with the atmosphere. For the diversity of existing empirical and process-based k models, the transfer velocity increases with the level of turbulence near the air–water interface. However, predictions for k can vary by a factor of 2 among different models. Near-surface turbulence results from the action of wind shear, surface waves, and buoyancy-driven convection. Wind shear has long been identified as a key driver, but recent lake studies have shifted the focus towards the role of convection, particularly in small lakes. In large lakes, wind fetch can, however, be long enough to generate surface waves and contribute to enhance gas transfer, as widely recognised in oceanographic studies. Here, field values for gas transfer velocity were computed in a large hard-water lake, Lake Geneva, from CO2 fluxes measured with an automated (forced diffusion) flux chamber and CO2 partial pressure measured with high-frequency sensors. k estimates were compared to a set of reference limnological and oceanic k models. Our analysis reveals that accounting for surface waves generated during windy events significantly improves the accuracy of k estimates in this large lake. The improved k model is then used to compute k over a 1-year time period. Results show that episodic extreme events with surface waves (6 % occurrence, significant wave height > 0.4 m) can generate more than 20 % of annual cumulative k and more than 25 % of annual net CO2 fluxes in Lake Geneva. We conclude that for lakes whose fetch can exceed 15 km, k models need to integrate the effect of surface waves.

In this paper, in the scope of a non-extensive statistical model for the nucleon’s structure function, the volume of the gluons in the nucleons and the relations among the temperature, T, the parameter “q” of Tsallis statistics, and the scattering energies, Q2, are studied. A system of equations with the usual sum rules are solved for the valence quarks, the experimental results for the polarized structure function, and the estimated carried moments for gluons and quarks. Each state of T and q leads to a set of chemical potentials and different radii for gluons and quarks. We conclude that gluons must occupy a larger volume than the quarks to fit the fraction of the total momentum. A linear function of the temperature with Q2 is obtained as an approach. The obtained range of temperatures is different from the previous models.

Let G(V,E) be a simple graph and f be a bijection f : V ∪ E → {1, 2, …, |V|+|E|} where f(V)={1, 2, …, |V|}. For a vertex x ∈ V, define its weight w(x) as the sum of labels of all edges incident with x and the vertex label itself. Then f is called a super vertex local antimagic total (SLAT) labeling if for every two adjacent vertices their weights are different. The super vertex local antimagic total chromatic number χslat(G) is the minimum number of colors taken over all colorings induced by super vertex local antimagic total labelings of G. We classify all trees T that have χslat(T)=2, present a class of trees that have χslat(T)=3, and show that for any positive integer n ≥ 2 there is a tree T with χslat(T)=n.

In this work, we investigate the Schrödinger dynamics of photon excitation numbers and entanglement in a system composed by two non-resonant time-dependent coupled oscillators. By considering π periodically pumped parameters (oscillator frequencies and coupling) and using suitable transformations, we show that the quantum dynamics can be determined by two classical Meissner oscillators. We then study analytically the stability of these differential equations and the dynamics of photon excitations and entanglement in the quantum system numerically. Our analysis shows two interesting results, which can be summarized as follows: (i) Classical instability of classical analog of quantum oscillators and photon excitation numbers (expectations Nj) are strongly correlated, and (ii) photon excitations and entanglement are connected to each other. These results can be used to shed light on the link between quantum systems and their classical counterparts and provide a nice complement to the existing works studying the dynamics of coupled quantum oscillators.

Phylogenetic trees are representations of the evolutionary descendency of a set of species. In graph-theoretic terms, a phylogenetic tree is a partially labeled tree where unlabeled vertices have at least degree three and labels corresponds to pairwise disjoint subsets of the set of species. A cut of a graph G = (V, E) is defined as bipartition {S, V \ S} of the vertex set V of G. A pair of cuts {S, S}, {T, T} is said to be crossing, if neither S ∩ T, S ∩ T, S ∩ T nor S ∩ T is empty. In this paper, we show that each set of pairwise non-crossing cuts of a graph G can be represented uniquely by a phylogenetic tree such that the set of species corresponds to the vertex set of G.

Two of the most studied graph labelings are the types of harmonious and graceful. A harmonious labeling of a graph of size m and order n, is an injective assignment of nonnegative integers smaller than m, such that the weights of the edges, which are defined as the sum of the labels of the end-vertices, are distinct consecutive integers after reducing modulo m. When n = m + 1, exactly two vertices of the graph have the same label. An α-labeling of a tree of size m is a bijective assignment of nonnegative integers, not larger than m, such that the labels on one stable set are smaller than the labels on the other stable set, and the weights of the edges, which are defined as the absolute difference of the labels of the end-vertices, are all distinct; this is the most restrictive type of graceful labeling. Even when these labelings are significantly different in their definitions of the weight, for certain kinds of graphs, there is a deep connection between harmonious and α-labelings. We present new families of harmoniously labeled graphs built on α-labeled trees. Among these new results there are three families of trees, the kth power of the path Pn, the join of a graph G and tK1 where G is a graph that admits a more restrictive type of harmonious labeling and its order is different of its size by at most one unit. We also prove the existence of two families of disconnected harmonius graphs: Kn, m ∪ K1, m − 1 and G ∪ T, where G is a unicyclic graph and T is a tree built with α-trees. In addition, we show that almost all trees admit a harmonious labeling.

Accurate Rayleigh scattering and absorption cross sections of atmospheric gases are essential for understanding the propagation of electromagnetic radiation in planetary atmospheres. Accurate extinction cross sections are also essential for calibrating high-finesse optical cavities and differential optical absorption spectroscopy and for accurate remote sensing. In this study, we measured the scattering and absorption cross sections of carbon dioxide, nitrous oxide, sulfur hexafluoride, oxygen, and methane in the continuous wavelength range of 307–725 nm using broadband cavity-enhanced spectroscopy (BBCES). The experimentally derived Rayleigh scattering cross sections for CO2, N2O, SF6, O2, and CH4 agree with refractive index-based calculations, with a difference of (0.4 ± 1.2) %, (−0.6 ± 1.1) %, (0.9 ± 1.4) %, (2.8 ± 1.2) %, and (0.9 ± 2.2) %, respectively. The O2–O2 collision-induced absorption and absorption by methane are obtained with high precision at the 0.8 nm resolution of our BBCES instrument in the 307–725 nm wavelength range. New dispersion relations for N2O, SF6, and CH4 were derived using data in the UV–vis wavelength range. This study provides dispersion relations for refractive indices, n-based Rayleigh scattering cross sections, and absorption cross sections based on more continuous and more extended wavelength ranges than available in the current literature.

For a finite commutative ring ℤn with identity 1 ≠ 0, the zero divisor graph Γ(ℤn) is a simple connected graph having vertex set as the set of non-zero zero divisors, where two vertices x and y are adjacent if and only if xy=0. We find the normalized Laplacian spectrum of the zero divisor graphs Γ(ℤn) for various values of n and characterize n for which Γ(ℤn) is normalized Laplacian integral. We also obtain bounds for the sum of graph invariant Sβ*(G)-the sum of the β-th power of the non-zero normalized Laplacian eigenvalues of Γ(ℤn).

A symmetric triple-hyperstar is a connected, 3-uniform hypergraph where, for some edge {a, b, c}, vertices a, b, and c all have degree k > 1 and all other edges contain exactly 2 vertices of degree 1. Let H denote the symmetric triple-hyperstar with 4 edges and, for positive integers λ and v, let λKv(3) denote the λ-fold complete 3-uniform hypergraph on v vertices. We find maximum packings of λKv(3) with copies of H.

Let Kn be a complete graph with n vertices. For graphs G and H, the Ramsey number R(G, H) is the smallest positive integer n such that in every red-blue coloring on the edges of Kn, there is a red copy of graph G or a blue copy of graph H in Kn. Determining the Ramsey number R(Cn, tWm) for any integers t ≥ 1, n ≥ 3 and m ≥ 4 in general is a challenging problem, but we conjecture that for any integers t ≥ 1 and m ≥ 4, there exists n0 = f(t, m) such that cycle Cn is tWm–good for any n ≥ n0. In this paper, we provide some evidence for the conjecture in the case of m = 4 that if n ≥ n0 then the Ramsey number R(Cn, tW4)=2n + t − 2 with n0 = 15t2 − 4t + 2 and t ≥ 1. Furthermore, if G is a disjoint union of cycles then the Ramsey number R(G, tW4) is also derived.

Indeterminacy associated with probing of a quantum state is commonly expressed through spectral distances (metric) featured in the outcomes of repeated experiments. Here we express it as an effective amount (measure) of distinct outcomes instead. The resulting $\mu$-uncertainties are described by the effective number theory [1] whose central result, the existence of a minimal amount, leads to a well-defined notion of intrinsic irremovable uncertainty. We derive $\mu$-uncertainty formulas for arbitrary set of commuting operators, including the cases with continuous spectra. The associated entropy-like characteristics, the $\mu$-entropies, convey how many degrees of freedom are effectively involved in a given measurement process. In order to construct quantum $\mu$-entropies, we are led to quantum effective numbers designed to count independent, mutually orthogonal states effectively comprising a density matrix. This concept is basis-independent and leads to a measure-based characterization of entanglement., Comment: 14 pages; v2: typos fixed, minor improvements; v3: 18 pages, appendices added, published version

We introduce a class of neighbourhood frames for graded modal logic embedding Kripke frames into neighbourhood frames. This class of neighbourhood frames is shown to be first-order definable but not modally definable. We also obtain a new definition of graded bisimulation with respect to Kripke frames by modifying the definition of monotonic bisimulation., Comment: removed journal template

Applicative bisimilarity is a coinductive characterisation of observational equivalence in call-by-name lambda-calculus, introduced by Abramsky in 1990. Howe (1989) gave a direct proof that it is a congruence. In previous work with Borthelle (2020), we abstract over this result by proposing a categorical framework for specifying operational semantics, in which we prove that (an abstract analogue of) applicative bisimilarity is automatically a congruence. However, the framework presents a few infelicities: (1) it requires a non-trivial refinement of the standard approach of Fiore, Plotkin, and Turi (1999) based on monoid algebras for specifying syntax with variable binding; (2) it relies on so-called prebisimulations instead of the more standard notion of bisimulation by lifting; (3) one of the axioms, called weak compositionality, feels ad hoc; (4) the proofs involve directed unions of relations, leading to quite a few painful inductions. In this paper, we rectify all of these deficiencies. In particular, a notable novelty is that the so-called Howe closure is defined as an initial monoid algebra in a category of spans. Finally, the familiality/cellularity axiom of the previous framework is now viewed as a mere sufficient condition for the main hypothesis, preservation of functional bisimulations.

We propose to simulate chemical reaction networks with the deterministic semantics abstractly, without any precise knowledge on the initial concentrations. For this, the concentrations of species are abstracted to booleans stating whether the species is present or absent, and the derivations of the concentrations are abstracted to signs saying whether the concentration is increasing, decreasing, or unchanged. We use abstract interpretation over the structure of signs for mapping the ODEs of a reaction network to a boolean network with nondeterministic updates. The abstract state transition graph of such boolean networks can be computed by finite domain constraint programming over the finite structure of signs. Constraints on the abstraction of the initial concentrations can be added naturally, leading to an abstract simulation algorithm that produces only the part of the abstract state transition graph that is reachable from the abstraction of the initial state. We proof the soundness of our abstract simulation algorithm, discuss how we implemented it, illustrate it usefulness for exact reasoning, and show its applicability to reaction networks in SBML format from the BioModels database.

Microphysical processes are important for the development of clouds and thus Earth's climate. For example, turbulent fluctuations in the water vapor mixing ratio, r, and temperature, T, cause fluctuations in the saturation ratio, S. Because S is the driving factor in the condensational growth of droplets, fluctuations may broaden the cloud droplet size distribution due to individual droplets experiencing different growth rates. The small-scale turbulent fluctuations in the atmosphere that are relevant to cloud droplets are difficult to quantify through field measurements. We investigate these processes in the laboratory using Michigan Tech's Π Chamber. The Π Chamber utilizes Rayleigh–Bénard convection (RBC) to create the turbulent conditions inherent in clouds. In RBC it is common for a large-scale circulation (LSC) to form. As a consequence of the LSC, the temperature field of the chamber is not spatially uniform. In this paper, we characterize the LSC in the Π Chamber and show how it affects the shape of the distributions of r, T, and S. The LSC was found to follow a single roll with an updraft and downdraft along opposing walls of the chamber. Near the updraft (downdraft), the distributions of T and r were positively (negatively) skewed. At each measuring position, S consistently had a negatively skewed distribution, with the downdraft being the most negative.

Fuzzy multiset is an extension of fuzzy set in multiset framework. In this paper, we review the concept of fuzzy multisets and study the notions of metric and norm on fuzzy multiset. Some results on metric and norm are established in fuzzy multiset context.

The ACl-ThCl4 (A = Li, Na, K) systems could be of relevance to the nuclear industry in the near future. A thermodynamic investigation of the three binary systems is presented herein. The excess Gibbs energy of the liquid solutions is described using the quasi-chemical formalism in the quadruplet approximation. The phase diagram optimisations are based on the experimental data available in the literature. The thermodynamic stability of the liquid solutions increases in the order Li < Na < K, in agreement with idealised interactions and structural models.

Bell’s inequality is investigated in parity-time (PT) symmetric quantum mechanics, using a recently developed form of the inequality by Maccone, with two PT-qubits in the unbroken phase with real energy spectrum. It is shown that the inequality produces a bound that is consistent with the standard quantum mechanics even after using Hilbert space equipped with CPT inner product and therefore, the entanglement has identical structure with standard quantum mechanics. Consequently, the no-signaling principle for a two-qubit system in PT-symmetric quantum theory is preserved.

By a molecular dynamics (MD) simulation method which ensures the system will be under hydrostatic pressure, dynamic and elastic properties of glassy metatstable states are investigated. In the MD method, the simulation cell fluctuates not only in volume but also in shape under constant hydrostatic pressure and temperature. As observed in experiments for many glass forming materials, metastable states in our simulation show a sharp increase in mean-square-displacement at certain temperatures TD. Dynamic heterogeneity is also observed at TD. Elastic properties are calculated from stress and strain relations obtained from the spontaneous fluctuation of internal stress tensor and simulation cell parameters. Each investigated state shows distinctive dynamics while maintaining solid-like elastic properties. The elastic properties stay intact even above TD. It has been shown that the rigidity and mobility of glassy metastable states are compatible under dynamic heterogeneity.

Motivated by the work on the domination number of directed de Bruijn graphs and some of its generalizations, in this paper we introduce a natural generalization of de Bruijn graphs (directed and undirected), namely $t$-constrained de Bruijn graphs, where $t$ is a positive integer, and then study the domination number of these graphs. Within the definition of $t$-constrained de Bruijn graphs, de Bruijn and Kautz graphs correspond to 1-constrained and 2-constrained de Bruijn graphs, respectively. This generalization inherits many structural properties of de Bruijn graphs and may have similar applications in interconnection networks or bioinformatics. We establish upper and lower bounds for the domination number on $t$-constrained de Bruijn graphs both in the directed and in the undirected case. These bounds are often very close and in some cases we are able to find the exact value.