Integer Weights Research Articles

Non-holomorphic modular flavor symmetry

The formalism of non-holomorphic modular flavor symmetry is developed, and the Yukawa couplings are level N polyharmonic Maaß forms satisfying the Laplacian condition. We find that the integer (even) weight polyharmonic Maaß forms of level N can be decomposed into multiplets of the finite modular group ΓN′\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {\\Gamma}_N^{\\prime } $$\\end{document} (ΓN). The original modular invariance approach is extended by the presence of negative weight polyharmonic Maaß forms. The non-holomorphic modular flavor symmetry can be consistently combined with the generalized CP symmetry. We present three example models for lepton sector based on the Γ3 ≅ A4 modular symmetry, the charged lepton masses and the neutrino oscillation data can be accommodated very well, and the predictions for the leptonic CP violation phases and the effective Majorana neutrino mass are studied.

Pediatric adapted risk index to predict 2-year transplant-related mortality post-HSCT in children

AbstractSeveral attempts have been made to optimize pretransplant risk assessment to improve hematopoietic stem cell transplantation (HSCT) decision-making and to predict post-HSCT outcomes. However, the relevance of pretransplant risk assessment to the pediatric population remains unclear. We report the results of revalidation of the hematopoietic cell transplantation comorbidity index (HCT-CI) in 874 children who received 944 HSCTs for malignant or nonmalignant diseases at a single center. After finding the HCT-CI invalid in our patient population, we proposed a modified pediatric adapted scoring system that captures risk factors (RFs) and comorbidities (CoMs) relevant to pediatrics. Each RF/CoM was assigned an integer weight based on its hazard ratio (HR) for transplant-related mortality (TRM): 0 (HR < 1.2), 1 (1.2 ≥ HR < 1.75), 2 (1.75 ≥ HR < 2.5), and 3 (HR ≥ 2.5). Using these weights, the pediatric adapted risk index (PARI) for HSCT was devised, and patients were divided into 4 risk groups (group 1: without RF/CoM; group 2: score 1-2; group 3: score 3-4; and group 4: score ≥5). There was a linear increase in 2-year TRM from group 1 to 4 (TRM, 6.2% in group 1, 50.9% in group 4). PARI was successfully validated on an internal and external cohort of pediatric patients. Comparing models using c-statistics, PARI was found to have better performance than HCT-CI in predicting 2-year TRM in children, with Akaike and Schwarz Bayesian information criteria values of 1069.245 and 1073.269, respectively, using PARI, vs 1223.158 and 1227.051, respectively, using HCT-CI. We believe that PARI will be a valuable tool enabling better counseling and decision-making for pediatric patients with HSCT.

Coalgebraic Satisfiability Checking for Arithmetic $\mu$-Calculi

The coalgebraic $\mu$-calculus provides a generic semantic framework for fixpoint logics over systems whose branching type goes beyond the standard relational setup, e.g. probabilistic, weighted, or game-based. Previous work on the coalgebraic $\mu$-calculus includes an exponential-time upper bound on satisfiability checking, which however relies on the availability of tableau rules for the next-step modalities that are sufficiently well-behaved in a formally defined sense; in particular, rule matches need to be representable by polynomial-sized codes, and the sequent duals of the rules need to absorb cut. While such rule sets have been identified for some important cases, they are not known to exist in all cases of interest, in particular ones involving either integer weights as in the graded $\mu$-calculus, or real-valued weights in combination with non-linear arithmetic. In the present work, we prove the same upper complexity bound under more general assumptions, specifically regarding the complexity of the (much simpler) satisfiability problem for the underlying one-step logic, roughly described as the nesting-free next-step fragment of the logic. The bound is realized by a generic global caching algorithm that supports on-the-fly satisfiability checking. Notably, our approach directly accommodates unguarded formulae, and thus avoids use of the guardedness transformation. Example applications include new exponential-time upper bounds for satisfiability checking in an extension of the graded $\mu$-calculus with polynomial inequalities (including positive Presburger arithmetic), as well as an extension of the (two-valued) probabilistic $\mu$-calculus with polynomial inequalities.

Theoretical studies of the [formula omitted]-strong Roman domination problem

The concept of Roman domination has been a subject of intrigue for more than two decades, with the fundamental Roman domination problem standing out as one of the most significant challenges in this field. This article studies a practically motivated generalization of this problem, known as the k-strong Roman domination. In this problem variant, defenders within a network are tasked with safeguarding any k vertices simultaneously, under multiple attacks. The aim is to find a feasible mapping that assigns a (integer) weight to each vertex of the input graph with a minimum sum of weights across all vertices. A function is considered feasible if any non-defended vertex, i.e. one labeled by zero, is protected by at least one of its neighboring vertices labeled by at least two. Furthermore, each defender ensures the safety of a non-defended vertex by imparting a value of one to it while retaining a one for themselves. To the best of our knowledge, this paper represents the first theoretical study on this problem. The study presents results for general graphs, establishes connections between the problem at hand and other domination problems, and provides exact values and bounds for specific graph classes, including complete graphs, paths, cycles, complete bipartite graphs, grids, and a few selected classes of convex polytopes. Additionally, an attainable lower bound for general cubic graphs is provided.

Q-A2NN: Quantized All-Adder Neural Networks for Onboard Remote Sensing Scene Classification

Performing remote sensing scene classification (RSSC) directly on satellites can alleviate data downlink burdens and reduce latency. Compared to convolutional neural networks (CNNs), the all-adder neural network (A2NN) is a novel basic neural network that is more suitable for onboard RSSC, enabling lower computational overhead by eliminating multiplication operations in convolutional layers. However, the extensive floating-point data and operations in A2NNs still lead to significant storage overhead and power consumption during hardware deployment. In this article, a shared scaling factor-based de-biasing quantization (SSDQ) method tailored for the quantization of A2NNs is proposed to address this issue, including a powers-of-two (POT)-based shared scaling factor quantization scheme and a multi-dimensional de-biasing (MDD) quantization strategy. Specifically, the POT-based shared scaling factor quantization scheme converts the adder filters in A2NNs to quantized adder filters with hardware-friendly integer input activations, weights, and operations. Thus, quantized A2NNs (Q-A2NNs) composed of quantized adder filters have lower computational and memory overheads than A2NNs, increasing their utility in hardware deployment. Although low-bit-width Q-A2NNs exhibit significantly reduced RSSC accuracy compared to A2NNs, this issue can be alleviated by employing the proposed MDD quantization strategy, which combines a weight-debiasing (WD) strategy, which reduces performance degradation due to deviations in the quantized weights, with a feature-debiasing (FD) strategy, which enhances the classification performance of Q-A2NNs through minimizing deviations among the output features of each layer. Extensive experiments and analyses demonstrate that the proposed SSDQ method can efficiently quantize A2NNs to obtain Q-A2NNs with low computational and memory overheads while maintaining comparable performance to A2NNs, thus having high potential for onboard RSSC.

Gap distributions of Fourier quasicrystals with integer weights via Lee–Yang polynomials

Recent work of Kurasov and Sarnak provides a method for constructing one-dimensional Fourier quasicrystals (FQ) from the torus zero sets of a special class of multivariate polynomials called Lee–Yang polynomials. In particular, they provided a non-periodic FQ with unit coefficients and uniformly discrete support, answering an open question posed by Meyer. Their method was later shown to generate all one-dimensional Fourier quasicrystals with \mathbb{N} -valued coefficients ( \mathbb{N} -FQ). In this paper, we characterize which Lee–Yang polynomials give rise to non-periodic \mathbb{N} -FQs with unit coefficients and uniformly discrete support, and show that this property is generic among Lee–Yang polynomials. We also show that the infinite sequence of gaps between consecutive atoms of any \mathbb{N} -FQ has a well-defined distribution, which, under mild conditions, is absolutely continuous. This generalizes previously known results for the spectra of quantum graphs to arbitrary \N -FQs. Two extreme examples are presented: first, a sequence of \mathbb{N} -FQs whose gap distributions converge to a Poisson distribution. Second, a sequence of random Lee–Yang polynomials that results in random \mathbb{N} -FQs whose empirical gap distributions converge to that of a random unitary matrix (CUE).

FairWASP: Fast and Optimal Fair Wasserstein Pre-processing

Recent years have seen a surge of machine learning approaches aimed at reducing disparities in model outputs across different subgroups. In many settings, training data may be used in multiple downstream applications by different users, which means it may be most effective to intervene on the training data itself. In this work, we present FairWASP, a novel pre-processing approach designed to reduce disparities in classification datasets without modifying the original data. FairWASP returns sample-level weights such that the reweighted dataset minimizes the Wasserstein distance to the original dataset while satisfying (an empirical version of) demographic parity, a popular fairness criterion. We show theoretically that integer weights are optimal, which means our method can be equivalently understood as duplicating or eliminating samples. FairWASP can therefore be used to construct datasets which can be fed into any classification method, not just methods which accept sample weights. Our work is based on reformulating the pre-processing task as a large-scale mixed-integer program (MIP), for which we propose a highly efficient algorithm based on the cutting plane method. Experiments demonstrate that our proposed optimization algorithm significantly outperforms state-of-the-art commercial solvers in solving both the MIP and its linear program relaxation. Further experiments highlight the competitive performance of FairWASP in reducing disparities while preserving accuracy in downstream classification settings.

Almost Envy-Free Allocations of Indivisible Goods or Chores with Entitlements

We here address the problem of fairly allocating indivisible goods or chores to n agents with weights that define their entitlement to the set of indivisible resources. Stemming from well-studied fairness concepts such as envy-freeness up to one good (EF1) and envy-freeness up to any good (EFX) for agents with equal entitlements, we present, in this study, the first set of impossibility results alongside algorithmic guarantees for fairness among agents with unequal entitlements. Within this paper, we expand the concept of envy-freeness up to any good or chore to the weighted context (WEFX and XWEF respectively), demonstrating that these allocations are not guaranteed to exist for two or three agents. Despite these negative results, we develop a WEFX procedure for two agents with integer weights, and furthermore, we devise an approximate WEFX procedure for two agents with normalized weights. We further present a polynomial-time algorithm that guarantees a weighted envy-free allocation up to one chore (1WEF) for any number of agents with additive cost functions. Our work underscores the heightened complexity of the weighted fair division problem when compared to its unweighted counterpart.

On Pareto optimal balanced exchanges

We investigate a market without money in which every agent offers indivisible goods in multiple copies, in exchange for goods of other agents. The exchange must be balanced in the sense that each agent should receive a quantity of good(s) equal to the one she transfers to others. We describe the market in graph-theoretic terms hence we use the notion of circulations to describe a balanced exchange of goods. Each agent has strict preferences over the agents from which she will receive goods and an upper bound on the quantity of each transaction, while a positive integer weight reflects the social importance of each unit exchanged. In this paper, we propose a simple variant of the Top Trading Cycles mechanism that finds a Pareto optimal circulation. We then offer necessary and sufficient conditions for a circulation to be Pareto optimal and, as a consequence, a easy recognition procedure. Last, we show that finding a maximum weight Pareto optimal circulation is NP-hard but becomes polynomial if weights are concordant with preferences.

Total Face Irregularity Strength of Certain Graphs

The edge k-labeling ψ of G is defined by a mapping from EG to a set of integers 1,2,…,k, where the integer weight assigned to the vertex x∈VG is given as wψx=∑ψxy, such that the sum is taken over every vertex of y∈VG that is adjacent to x and the integer weights of adjacent vertices must be distinct for all vertices with x≠y. An irregular assignment of G using atmost k labels which is considered to be a minimum k is defined as irregularity strength of a graph G and can be denoted as sG. There are also further works on familiar irregular assignments, such as edge irregular labelings, vertex irregular total labelings, edge irregular total labelings, and face irregular entire k-labelings of plane graphs. A plane graph can be defined as a graph that is embedded in the plane in which no two lines will be intersected. In a plane graph the number of regions present are called faces and we denote it as F. The concept of total face irregularity strength is defined by the motivation of irregular networks and entire irregular face k-labeling. In our paper, we have obtained a minimum bound for the total face irregularity strength of two-connected plane graphs like cycle-of-ladder, C-necklace graph, P-necklace graph, sibling tree, and triangular graph.

Utilizing Fractional Artificial Neural Networks for Modeling Cancer Cell Behavior

In this paper, a novel approach involving a fractional recurrent neural network (RNN) is proposed to achieve the observer-based synchronization of a cancer cell model. According to the properties of recurrent neural networks, our proposed framework serves as a predictive method for the behavior of fractional-order chaotic cancer systems with uncertain orders. Through a stability analysis of weight updating laws, we design a fractional-order Nonlinear Autoregressive with Exogenous Inputs (NARX) network, in which its learning algorithm demonstrates admissible and faster convergence. The main contribution of this paper lies in the development of a fractional neural observer for the fractional-order cancer systems, which is robust in the presence of uncertain orders. The proposed fractional-order model for cancer can capture complex and nonlinear behaviors more accurately than traditional integer-order models. This improved accuracy can provide a more realistic representation of cancer dynamics. Simulation results are presented to demonstrate the effectiveness of the proposed method, where mean square errors of synchronization by applying integer and fractional weight matrix laws are calculated. The density of tumor cell, density of healthy host cell and density of effector immune cell errors for the observer-based synchronization of fractional-order (OSFO) cancer system are less than 0.0.0048, 0.0062 and 0.0068, respectively. Comparative tables are provided to validate the improved accuracy achieved by the proposed framework.

Heuristic approach for bandwidth consecutive multi-coloring problem

Bandwidth consecutive multicoloring problem is also known as a b-coloring problem. Let G = (V, E) be a graph where V is the set of vertices and E is the set of edges. Let each vertex v of V has a positive integer weight b (v) and each edge (v, w) of E has a non-negative integer weight b (v, w). A bandwidth consecutive multicoloring of a graph is a problem of assigning b (v) consecutive positive integers to each vertex v of V in such a manner that the difference between all the integers of vertex v and all the integers of vertex w is greater than b (v, w). The maximum integer assigned in this coloring is called the span of the coloring. The b-coloring is the problem of minimizing this span. No metaheuristic is proposed for general graphs so far for this problem till date as it is strongly NP-hard. In this paper, we proposed three heuristics for the problem including a greedy randomized adaptive search procedure (GRASP). The efficiency of these algorithms is tested on benchmark graphs and their performance is compared among themselves. Experimental results showed that among all three proposed heuristics, GRASP performed well for the given problem.

Improving Differential Interferometry Synthetic Aperture Radar Phase Unwrapping Accuracy with Global Navigation Satellite System Monitoring Data

: We developed a GNSS-assisted InSAR phase unwrapping algorithm for large-deformation DInSAR data processing in coal mining areas. Utilizing the Markov random field (MRF) theory and simulated annealing, the algorithm derived the energy function using MRF theory, Gibbs distribution, and the Hammersley–Clifford theorem. It calculated an image probability ratio and unwrapped the phase through iterative calculations of the initial integer perimeter matrix, interference phase, and weight matrix. Algorithm reliability was confirmed by combining simulated phases with digital elevation model (DEM) data for deconvolution calculations, showing good agreement with real phase-value results (median error: 4.8 × 10−4). Applied to ALOS-2 data in the Jinfeng mining area, the algorithm transformed interferometric phase into deformation, obtaining simulated deformation by fitting GNSS monitoring data. It effectively solved meter-scale deformation variables between single-period images, particularly for unwrapping problems due to decoherence. To improve calculation speed, a coherence-based threshold was set. Points with high coherence avoided iterative optimization, while points below the threshold underwent iterative optimization (coherence threshold: 0.32). The algorithm achieved a median error of 30.29 mm and a relative error of 2.5% compared to GNSS fitting results, meeting accuracy requirements for mining subsidence monitoring in large mining areas.

The possible winner with uncertain weights problem

The original possible winner problem consists of an unweighted election with partial preferences and a distinguished candidate c and asks whether the preferences can be extended to total ones such that c wins the given election. We introduce a novel variant of this problem: possible winner with uncertain weights. In this variant, for a given weighted election, not some of the preferences but some of the preferences' weights are uncertain. We introduce a general framework to study this problem for nonnegative integer and rational weights as well as for four different variations of the problem itself: with and without given upper bounds on the total weight and with and without given ranges to choose weights from. We study the complexity of these problems for important voting systems such as scoring protocols, (simplified) Bucklin and fallback voting, plurality with runoff and veto with runoff, Copelandα, ranked pairs, and Borda.

Secure and efficient implementation of facial emotion detection for smart patient monitoring system

BackgroundMachine learning has enabled the automatic detection of facial expressions, which is particularly beneficial in smart monitoring and understanding the mental state of medical and psychological patients. Most algorithms that attain high emotion classification accuracy require extensive computational resources, which either require bulky and inefficient devices or require the sensor data to be processed on cloud servers. However, there is always the risk of privacy invasion, data misuse, and data manipulation when the raw images are transferred to cloud servers for processing facical emotion recognition (FER) data. One possible solution to this problem is to minimize the movement of such private data.MethodsIn this research, we propose an efficient implementation of a convolutional neural network (CNN) based algorithm for on‐device FER on a low‐power field programmable gate array (FPGA) platform. This is done by encoding the CNN weights to approximated signed digits, which reduces the number of partial sums to be computed for multiply‐accumulate (MAC) operations. This is advantageous for portable devices that lack full‐fledged resource‐intensive multipliers.ResultsWe applied our approximation method on MobileNet‐v2 and ResNet18 models, which were pretrained with the FER2013 dataset. Our implementations and simulations reduce the FPGA resource requirement by at least 22% compared to models with integer weight, with negligible loss in classification accuracy.ConclusionsThe outcome of this research will help in the development of secure and low‐power systems for FER and other biomedical applications. The approximation methods used in this research can also be extended to other image‐based biomedical research fields.

The maximum spectral radius of the weighted bicyclic hypergraphs

Let B n , k , a be the set of weighted k-uniform connected bicyclic hypergraphs of order n with positive integer weights and fixed total weight sum a, where n, k and a are positive integers with k ≥ 4 and a ≥ n + 1 k − 1 ≥ 3 . An α-normal labelling method is proposed for comparing the spectral radii of the weighted hypergraphs under consideration. The weighted hypergraph having the maximum spectral radius among the hypergraps in B n , k , a is obtained.

Growth of Fourier coefficients of vector-valued automorphic forms

In this article, we establish polynomial-growth bound for the sequence of Fourier coefficients associated with even integer weight vector-valued automorphic forms of non-cocompact Fuchsian groups of the first kind. In the end, their L-functions and exponential sums have been discussed.

Subcubic Equivalences between Graph Centrality Problems, APSP, and Diameter

Measuring the importance of a node in a network is a major goal in the analysis of social networks, biological systems, transportation networks, and so forth. Different centrality measures have been proposed to capture the notion of node importance. For example, the center of a graph is a node that minimizes the maximum distance to any other node (the latter distance is the radius of the graph). The median of a graph is a node that minimizes the sum of the distances to all other nodes. Informally, the betweenness centrality of a node w measures the fraction of shortest paths that have w as an intermediate node. Finally, the reach centrality of a node w is the smallest distance r such that any s - t shortest path passing through w has either s or t in the ball of radius r around w . The fastest known algorithms to compute the center and the median of a graph and to compute the betweenness or reach centrality even of a single node take roughly cubic time in the number n of nodes in the input graph. It is open whether these problems admit truly subcubic algorithms, i.e., algorithms with running time Õ(n 3-δ ) for some constant δ &gt; 0. 1 We relate the complexity of the mentioned centrality problems to two classical problems for which no truly subcubic algorithm is known, namely All Pairs Shortest Paths (APSP) and Diameter. We show that Radius, Median, and Betweenness Centrality are equivalent under subcubic reductions to APSP, i.e., that a truly subcubic algorithm for any of these problems implies a truly subcubic algorithm for all of them. We then show that Reach Centrality is equivalent to Diameter under subcubic reductions. The same holds for the problem of approximating Betweenness Centrality within any finite factor. Thus, the latter two centrality problems could potentially be solved in truly subcubic time, even if APSP required essentially cubic time. On the positive side, our reductions for Reach Centrality imply an improved Õ(Mn ω )-time algorithm for this problem in case of non-negative integer weights upper bounded by M , where ω is a fast matrix multiplication exponent.

Electronic Nose Pattern Recognition Engine: Design, Build, and Deployment

The electronic nose (e-nose) consists of a sensor array, a pattern recognition engine, and peripheral circuitry, where the pattern recognition engine performs gas classification. The low-power consumption, miniaturization, and high-speed response of the pattern recognition engine are important for the application of e-nose. Several researchers have applied deep learning to e-noses’ pattern recognition engines and achieved high recognition rates. However, neural networks with high recognition rates usually have complicated structures and a huge number of parameters, which seriously hinder the deployment of e-nose on end-side devices. This article proposes a hybrid precision quantization algorithm to solve this problem, which quantizes the neural network by reserving both floating point and integer weights. Based on this, we build a hardware-friendly lightweight gas classification neural network (HFL-GCNN) model. The model can reduce the storage space and computing resources required for device while maintaining high inference accuracy. In addition, we designed a gas data acquisition system for model training and verification. Considering the completeness of the work, we designed a convolution computing accelerator based on field programmable gate array (FPGA). We deployed the neural network model to the FPGA device, which ultimately realized the design, build, and deployment of the e-nose pattern recognition engine. The experimental results show that the model proposed in this article can achieve a recognition accuracy of 99.23% when classifying ten types of gases with lower power consumption and delay. The work can provide a new idea for the application of e-nose.

Sum-of-Max partition under a Knapsack constraint

Sequence partition problems arise in many fields, such as sequential data analysis, information transmission, and parallel computing. In this paper, we study the following partition problem variant: given a sequence of n items 1,…,n, where each item i is associated with weight wi and another parameter si, partition the sequence into several consecutive subsequences, so that the total weight of each subsequence is no more than a threshold w0, and the sum of the largest si in each subsequence is minimized.This problem admits a straightforward solution based on dynamic programming, which costs O(n2) time and can be improved to O(nlogn) time easily. Our contribution is an O(n) time algorithm, which is nontrivial yet easy to implement. We also study the corresponding tree partition problem. We prove that the problem on the tree is NP-complete and we present an O(w0n2) time (O(w02n2) time, respectively) algorithm for the unit weight (integer weight, respectively) case.