Search

In this work, we present a novel Koopman spectrum-based reachability verification method for nonlinear systems. Contrary to conventional methods that focus on characterizing all potential states of a dynamical system over a presupposed time span, our approach seeks to verify the reachability by assessing the non-emptiness of estimated time-to-reach intervals without engaging in the explicit computation of reachable set. Based on the spectral analysis of the Koopman operator, we reformulate the problem of verifying existence of reachable trajectories into the problem of determining feasible time-to-reach bounds required for system reachability. By solving linear programming (LP) problems, our algorithm can effectively estimate all potential time intervals during which a dynamical system can enter (and exit) target sets from given initial sets over an unbounded time horizon. Finally, we demonstrate our method in challenging settings, such as verifying the reachability between non-convex or even disconnected sets, as well as backward reachability and multiple entries into target sets. Additionally, we validate its applicability in addressing real-world challenges and scalability to high-dimensional systems through case studies in verifying the reachability of the cart-pole and multi-agent consensus systems., Comment: This work has been submitted to the IEEE for possible publication

A partition is said to be $\ell$-regular if none of its parts is a multiple of $\ell$. Let $b^\prime_5(n)$ denote the number of 5-regular partitions into distinct parts (equivalently, into odd parts) of $n$. This function has also close connections to representation theory and combinatorics. In this paper, we study arithmetic properties of $b^\prime_5(n)$. We provide full characterization of the parity of $b^\prime_5(2n+1)$, present several congruences modulo 4, and prove that the generating function of the sequence $(b^\prime_5(5n+1))$ is lacunary modulo any arbitrary positive powers of 5., Comment: To appear in the International Journal of Number Theory

We prove some new modular identities for the Rogers\textendash Ramanujan continued fraction. For example, if $R(q)$ denotes the Rogers\textendash Ramanujan continued fraction, then \begin{align*}&R(q)R(q^4)=\dfrac{R(q^5)+R(q^{20})-R(q^5)R(q^{20})}{1+R(q^{5})+R(q^{20})},\\ &\dfrac{1}{R(q^{2})R(q^{3})}+R(q^{2})R(q^{3})= 1+\dfrac{R(q)}{R(q^{6})}+\dfrac{R(q^{6})}{R(q)}, \end{align*}and\begin{align*}R(q^2)=\dfrac{R(q)R(q^3)}{R(q^6)}\cdot\dfrac{R(q) R^2(q^3) R(q^6)+2 R(q^6) R(q^{12})+ R(q) R(q^3) R^2(q^{12})}{R(q^3) R(q^6)+2 R(q) R^2(q^3) R(q^{12})+ R^2(q^{12})}.\end{align*} In the process, we also find some new relations for the Rogers-Ramanujan functions by using dissections of theta functions and the quintuple product identity., Comment: To appear in Journal of the Korean Mathematical Society

Code-domain non-orthogonal multiple access (CD-NOMA) systems offer key benefits such as high spectral efficiency, low latency, high reliability, and massive connectivity. NOMA's ability to handle overloading allows multiple devices to share a single resource element (RE) for data transmission. In CD-NOMA, different users are assigned distinct codewords, which are leveraged during multi-user detection (MUD). Codebook-based NOMA systems outperform spread-sequence (SS)-based NOMA due to the coding gains provided by the codebooks. Sparse code multiple access (SCMA) and dense code multiple access (DCMA) are two prominent examples of such systems. Additionally, NOMA is seen as a crucial technology for enabling grant-free access, especially in massive machine-type communications (mMTC). One of the main challenges in deploying grant-free NOMA systems is accurately detecting both user activity and transmitted data, particularly when user activity fluctuates dynamically across the transmission frame. This paper introduces codebook-based grant-free NOMA systems modeled using a block sparsity signal structure. The joint activity and data detection (JADD) problem in these systems is formulated as group LASSO and sparse group LASSO block compressive sensing (BCS) problems. To address these, a robust prior information-aided alternating direction method of multipliers (ADMM) algorithm is proposed. Extensive numerical experiments and theoretical analysis show the efficiency of the proposed algorithm, making it a suitable solution for mMTC networks.

Constrained optimization problems arise in various engineering system operations such as inventory management and electric power grids. However, the requirement to repeatedly solve such optimization problems with uncertain parameters poses a significant computational challenge. This work introduces a learning scheme using Bayesian Neural Networks (BNNs) to solve constrained optimization problems under limited labeled data and restricted model training times. We propose a semi-supervised BNN for this practical but complex regime, wherein training commences in a sandwiched fashion, alternating between a supervised learning step (using labeled data) for minimizing cost, and an unsupervised learning step (using unlabeled data) for enforcing constraint feasibility. Both supervised and unsupervised steps use a Bayesian approach, where Stochastic Variational Inference is employed for approximate Bayesian inference. We show that the proposed semi-supervised learning method outperforms conventional BNN and deep neural network (DNN) architectures on important non-convex constrained optimization problems from energy network operations, achieving up to a tenfold reduction in expected maximum equality gap and halving the optimality and inequality (feasibility) gaps, without requiring any correction or projection step. By leveraging the BNN's ability to provide posterior samples at minimal computational cost, we demonstrate that a Selection via Posterior (SvP) scheme can further reduce equality gaps by more than 10%. We also provide tight and practically meaningful probabilistic confidence bounds that can be constructed using a low number of labeled testing data and readily adapted to other applications.

Antiferromagnets that display very small stray magnetic field are ideal for spintronic applications. Of particular interest are non-collinear, chiral antiferromagnets of the type Mn3X (X=Sn, Ge), which display a large magnetotransport response that is correlated with their antiferromagnetic ordering. The ability to read out and manipulate this ordering is crucial for their integration into spintronic devices. These materials exhibit a tiny unbalanced magnetic moment such that a large external magnetic field can, in principle, be used to set the material into a single antiferromagnetic domain. However, in thin films of Mn3Sn, we find that such fields induce only a partial magnetic ordering. By detecting two orthogonal in-plane components of the magnetic order vector, we find that the non-switchable fraction has a unidirectional anisotropy. This also enables us to visualize switching along multiple easy axes in Mn3Sn. Studying the switching at the nanoscale allows us to correlate the pining behavior to crystal grain boundaries in the Mn3Sn nanowire structures.

Recently, Gireesh, Ray, and Shivashankar studied an analog, $\overline{a}_t(n)$, of the $t$-core partition function, $c_t(n)$. In this paper, we study the function $\overline{a}_5(n)$ in conjunction with $c_5(n)$ as well as another analogous function $\overline{b}_5(n)$. We also find several arithmetic identities for $\overline{a}_5(n)$ and $\overline{b}_5(n)$., Comment: 15 pages

Recently, Jha (arXiv:2007.04243, arXiv:2011.11038) has found identities that connect certain sums over the divisors of $n$ to the number of representations of $n$ as a sum of squares and triangular numbers. In this note, we state a generalized result that gives such relations for $s$-gonal numbers for any integer $s\geq3$., Comment: 8 pages

Recently, Merca and Schmidt found some decompositions for the partition function $p(n)$ in terms of the classical M\"{o}bius function as well as Euler's totient. In this paper, we define a counting function $T_k^r(m)$ on the set of $n$-color partitions of $m$ for given positive integers $k, r$ and relate the function with the $n$-color partition function and other well-known arithmetic functions like the M\"obius function, Liouville function, etc. and their divisor sums. Furthermore, we use a counting method of Erd\"os to obtain some counting theorems for $n$-color partitions that are analogous to those found by Andrews and Deutsch for the partition function., Comment: 14 pages

We present the second data release of the MeerKAT Absorption Line Survey (MALS), consisting of wideband continuum catalogues of 391 pointings observed at L~band. The full wideband catalogue covers 4344 deg$^2$ of sky, reaches a depth of 10 $\mu$Jy beam$^{-1}$, and contains 971,980 sources. With its balance between survey depth and sky coverage, MALS DR2 covers five orders of magnitude of flux density, presenting a robust view of the extragalactic radio source population down to 200 $\mu$Jy. Using this catalogue, we perform a measurement of the cosmic radio dipole, an anisotropy in the number counts of radio sources with respect to the cosmic background, analogous to the dipole found in the cosmic microwave background (CMB). For this measurement, we present the characterisation of completeness and noise properties of the catalogue, and show that a declination-dependent systematic affects the number density of faint sources. In the dipole measurement on the MALS catalogue, we recover reasonable dipole measurements once we model the declination systematic with a linear fit between the size of the major axis of the restoring beam and the amount of sources of each pointing. The final results are consistent with the CMB dipole in terms of direction and amplitude, unlike many recent measurements of the cosmic radio dipole made with other centimetre wavelength catalogues, which generally show a significantly larger amplitude. This result demonstrates the value of dipole measurements with deeper and more sparse radio surveys, as the population of faint sources probed may have had a significant impact on the measured dipole., Comment: 25 pages, 14 figures. Accepted for publication in Astronomy & Astrophysics. The MALS wideband catalogues and images are publicly available at https://mals.iucaa.in

Cyber-attack attribution is an important process that allows experts to put in place attacker-oriented countermeasures and legal actions. The analysts mainly perform attribution manually, given the complex nature of this task. AI and, more specifically, Natural Language Processing (NLP) techniques can be leveraged to support cybersecurity analysts during the attribution process. However powerful these techniques are, they need to deal with the lack of datasets in the attack attribution domain. In this work, we will fill this gap and will provide, to the best of our knowledge, the first dataset on cyber-attack attribution. We designed our dataset with the primary goal of extracting attack attribution information from cybersecurity texts, utilizing named entity recognition (NER) methodologies from the field of NLP. Unlike other cybersecurity NER datasets, ours offers a rich set of annotations with contextual details, including some that span phrases and sentences. We conducted extensive experiments and applied NLP techniques to demonstrate the dataset's effectiveness for attack attribution. These experiments highlight the potential of Large Language Models (LLMs) capabilities to improve the NER tasks in cybersecurity datasets for cyber-attack attribution., Comment: Submitted to WISE 2024

In this work, we investigate the implications of the differential Hebbian learning rule known as Input-Correlations (ICO) learning in the classification of synchronization in coupled nonlinear oscillator systems. We are investigating the parity-time symmetric coupled Duffing oscillator system with nonlinear dissipation/amplification. In our investigation of the temporal dynamics of this system, it is observed that the system exhibits chaotic as well as quasiperiodic dynamics. On further investigation, it is found that the chaotic dynamics is distorted anti-phase synchronized, whereas the quasiperiodic dynamics is desynchronized. So, on the application of the ICO learning in these two parametric regimes, we observe that the weight associated with the stimulus remains constant when the oscillators are anti-phase synchronized, in spite of there being distortion in the synchronization. But when the oscillators exhibit quasiperiodic dynamics, there is erratic evolution of the weight with time. So, from this, it could be ascertained that the ICO learning could be made use of in the classification of synchronization dynamics in nonlinear systems., Comment: 6 pages, 5 figures

Intelligent reflecting surface (IRS) technology has become a crucial enabler for creating cost effective, innovative, and adaptable wireless communication environments. This study investigates an IRS-assisted orthogonal time frequency space (OTFS) modulation that facilitates communication between users and the base station (BS). The users attainable downlink rate can be boosted by collaboratively improving the reflection coefficient (RC) matrix at the IRS and beamforming matrix at the BS. Then, in the IRS-aided OTFS network, the problem of cooperative precoding at BS and IRS to improve the network throughput is framed. The precoding design problem is non-convex and highly complicated; an alternate optimization (AO) approach is proposed to solve this. Specifically, an approach based on strongest tap maximization (STM) and fractional programming is proposed. It solves RC matrix (at IRS) and beamforming matrix (at BS) alternatively. Moreover, an efficient signal detector for IRS-aided OTFS communication systems using the alternating direction method of multipliers (ADMM) is proposed. Finally, to estimate the cascaded MIMO channel, using a parallel factor tensor model that separates the IRS-User and BS-IRS MIMO channels, respectively is suggested. Simulation results show that the proposed method significantly enhances the system capacity and bit error rate (BER) performance compared to conventional OTFS., Comment: Submitted to an IEEE journal, 30 pages, single column

The anomalous Nernst effect (ANE) gives rise to an electrical response transverse to the magnetization and an applied temperature gradient in a magnetic metal. A nanoscale temperature gradient can be generated by the use of a laser beam applied to the apex of an atomic force microscope tip, thereby allowing for spatially-resolved ANE measurements beyond the optical diffraction limit. Such a method has been used previously to map in-plane magnetized magnetic textures. However, the spatial distribution of the out-of-plane temperature gradient, which is needed to fully interpret such an ANE-based imaging, was not studied. We therefore use a well-known magnetic texture, a magnetic vortex core, to demonstrate the reliability of the ANE method for the imaging of magnetic domains with nanoscale resolution. Moreover, since the ANE signal is directly proportional to the temperature gradient, we can also consider the inverse problem and deduce information about the nanoscale temperature distribution. Our results together with finite element modeling indicate that besides the out-of-plane temperature gradients, there are even larger in-plane temperature gradients. Thus we extend the ANE imaging to study out-of-plane magnetization in a racetrack nano-wire by detecting the ANE signal generated by in-plane temperature gradients. In all cases, a spatial resolution of about 80 nm is obtained. These results are significant for the rapidly growing field of thermo-electric imaging of antiferromagnetic spintronic device structures.

We explore the production of thermal dark matter (DM) candidates (WIMPs, SIMPs, ELDERs and Cannibals) during cosmic reheating. Assuming a general parametrization for the scaling of the inflaton energy density and the standard model (SM) temperature, we study the requirements for kinetic and chemical DM freeze-out in a model-independent way. For each of the mechanisms, up to two solutions that fit the entire observed DM relic density exist, for a given reheating scenario and DM mass. As an example, we assume a simple particle physics model in which DM interacts with itself and with SM through contact interactions. We find that low-temperature reheating can accommodate a wider range of couplings and larger masses than those permitted in the usual instantaneous high-temperature reheating. This results in DM solutions for WIMPs reaching masses as high as $10^{14}$~GeV, whereas for SIMPs and ELDERs, we can reach masses of $10^{13}$~GeV. Interestingly, current experimental data already constrain the enlarged parameter space of these models with low-reheating temperatures. Next-generation experiments could further probe these scenarios., Comment: 34 pages, 16 figures, To appear in JCAP

Security properties of real-time systems often involve reasoning about hyper-properties, as opposed to properties of single executions or trees of executions. These hyper-properties need to additionally be expressive enough to reason about real-time constraints. Examples of such properties include information flow, side channel attacks and service-level agreements. In this paper we study computational problems related to a branching-time, hyper-property extension of metric temporal logic (MTL) that we call HCMTL*. We consider both the interval-based and point-based semantics of this logic. The verification problem that we consider is to determine if a given HCMTL* formula $\varphi$ is true in a system represented by a timed automaton. We show that this problem is undecidable. We then show that the verification problem is decidable if we consider executions upto a fixed time horizon $T$. Our decidability result relies on reducing the verification problem to the truth of an MSO formula over reals with a bounded time interval.

In this article, we investigate the implications of the unsupervised learning rule known as Input-Correlations (ICO) learning in the nonlinear dynamics of two linearly coupled PT-symmetric Li\'enard oscillators. The fixed points of the oscillator have been evaluated analytically and the Jacobian linearization is employed to study their stability. We find that on increasing the amplitude of the external periodic drive, the system exhibits period-doubling cascade to chaos within a specific parametric regime wherein we observe emergent chaotic dynamics. We further notice that the system indicates an intermittency route to chaos in the chaotic regime. Finally, in the period-4 regime of our bifurcation analysis, we predict the emergence of transient chaos which eventually settles down to a period-2 oscillator response which has been further validated by both the maximal Finite-Time Lyapunov Exponent (FTLE) using the well-known Gram-Schmidt orthogonalization technique and the Hilbert Transform of the time-series. In the transiently chaotic regime, we deploy the ICO learning to analyze the time-series from which we identify that when the chaotic evolution transforms into periodic dynamics, the synaptic weight associated with the time-series of the loss oscillator exhibits stationary temporal evolution. This signifies that in the periodic regime, there is no overlap between the filtered signals obtained from the time-series of the coupled PT-symmetric oscillators. In addition, the temporal evolution of the weight associated with the stimulus mimics the behaviour of the Hilbert transform of the time-series., Comment: 9 pages, 12 figures

We investigate the temporal dynamics of the Ikeda Map with Balanced Gain and Loss and in the presence of feedback loops with saturation nonlinearity. From the bifurcation analysis, we find that the temporal evolution of optical power undergoes period quadrupling at the exceptional point (EP) of the system and beyond that, chaotic dynamics emerge in the system and this has been further corroborated from the Largest Lyapunov Exponent (LLE) of the model. For a closer inspection, we analyzed the parameter basin of the system, which further leads to our inference that the Ikeda Map with Balanced Gain and Loss exhibits the emergence of chaotic dynamics beyond the exceptional point (EP). Furthermore, we find that the temporal dynamics beyond the EP regime leads to the onset of Extreme Events (EE) in this system via attractor merging crisis.

We introduce OpenBot-Fleet, a comprehensive open-source cloud robotics system for navigation. OpenBot-Fleet uses smartphones for sensing, local compute and communication, Google Firebase for secure cloud storage and off-board compute, and a robust yet low-cost wheeled robot toact in real-world environments. The robots collect task data and upload it to the cloud where navigation policies can be learned either offline or online and can then be sent back to the robot fleet. In our experiments we distribute 72 robots to a crowd of workers who operate them in homes, and show that OpenBot-Fleet can learn robust navigation policies that generalize to unseen homes with >80% success rate. OpenBot-Fleet represents a significant step forward in cloud robotics, making it possible to deploy large continually learning robot fleets in a cost-effective and scalable manner. All materials can be found at https://www.openbot.org. A video is available at https://youtu.be/wiv2oaDgDi8, Comment: Accepted at ICRA'24

Malnutrition among newborns is a top public health concern in developing countries. Identification and subsequent growth monitoring are key to successful interventions. However, this is challenging in rural communities where health systems tend to be inaccessible and under-equipped, with poor adherence to protocol. Our goal is to equip health workers and public health systems with a solution for contactless newborn anthropometry in the community. We propose NurtureNet, a multi-task model that fuses visual information (a video taken with a low-cost smartphone) with tabular inputs to regress multiple anthropometry estimates including weight, length, head circumference, and chest circumference. We show that visual proxy tasks of segmentation and keypoint prediction further improve performance. We establish the efficacy of the model through several experiments and achieve a relative error of 3.9% and mean absolute error of 114.3 g for weight estimation. Model compression to 15 MB also allows offline deployment to low-cost smartphones., Comment: Accepted at CVPM Workshop at CVPR 2024

In this work, we investigated the spatial evolution of optical power in a closed-form optical waveguide configuration consisting of six passive waveguides and each of the waveguides exhibits equal strength of Kerr nonlinearity. We considered only nearest neighbor interaction between the waveguides. We found that in the case of low Kerr nonlinearity, evolution of optical power shows synchronization behavior. But when we increased the strength of Kerr nonlinearity, we discovered that spatial evolution of optical power in all waveguides shows independent characteristics. On the other hand, we have studied the impact of the coupling constant on the synchronization dynamics of our system. Our findings showed us that strong coupling can strengthen the collective dynamics in the presence of strong Kerr nonlinearity. From our results, we can conclude that Kerr nonlinearity in our system plays the role of disorder parameter that destroys as well as alters the synchronization behavior of evolution of optical power in the waveguides and coupling constant plays the role of an antagonist and restores synchronization in the model., Comment: 7 pages, 6 figures

Accurate and timely detection of cyber threats is critical to keeping our online economy and data safe. A key technique in early detection is the classification of unusual patterns of network behaviour, often hidden as low-frequency events within complex time-series packet flows. One of the ways in which such anomalies can be detected is to analyse the information entropy of the payload within individual packets, since changes in entropy can often indicate suspicious activity - such as whether session encryption has been compromised, or whether a plaintext channel has been co-opted as a covert channel. To decide whether activity is anomalous we need to compare real-time entropy values with baseline values, and while the analysis of entropy in packet data is not particularly new, to the best of our knowledge there are no published baselines for payload entropy across common network services. We offer two contributions: 1) We analyse several large packet datasets to establish baseline payload information entropy values for common network services, 2) We describe an efficient method for engineering entropy metrics when performing flow recovery from live or offline packet data, which can be expressed within feature subsets for subsequent analysis and machine learning applications., Comment: 14 pages, 8 figures

The effect of metallicity on the theoretical and empirical period-luminosity (PL) relations of Cepheid variables is not well understood and remains a highly debated issue. Here, we examine empirical colour-magnitude diagrams (CMDs) of Classical and Type-II Cepheids in the Magellanic Clouds and compare those with the theoretically predicted instability strip (IS) edges. We explore the effects of incorporating turbulent flux, turbulent pressure, and radiative cooling into the convection theory on the predicted IS at various metallicities using MESA-RSP. We find that the edges become redder with the increasing complexity of convection physics incorporated in the fiducial convection sets, and are similarly shifted to the red with increasing metallicity. The inclusion of turbulent flux and pressure improves the agreement of the red edge of the IS, while their exclusion leads to better agreement with observations of the blue edge. About 90% of observed stars are found to fall within the predicted bluest and reddest edges across the considered variations of turbulent convection parameters. Furthermore, we identify and discuss discrepancies between theoretical and observed CMDs in the low effective temperature and high luminosity regions for stars with periods greater than ~ 20 days. These findings highlight the potential for calibrating the turbulent convection parameters in stellar pulsation models or the prediction of a new class of rare, long-period, 'red Cepheids', thereby improving our understanding of Cepheids and their role in cosmological studies., Comment: Accepted for publication in MNRAS on 25-04-2024. 19 pages, 15 figures, 8 tables

The Multiple Traveling Salesman Problem (MTSP) with a single depot is a generalization of the well-known Traveling Salesman Problem (TSP) that involves an additional parameter, namely, the number of salesmen. In the MTSP, several salesmen at the depot need to visit a set of interconnected targets, such that each target is visited precisely once by at most one salesman while minimizing the total length of their tours. An equally important variant of the MTSP, the min-max MTSP, aims to distribute the workload (length of the individual tours) among salesmen by requiring the longest tour of all the salesmen to be as short as possible, i.e., minimizing the maximum tour length among all salesmen. The min-max MTSP appears in real-life applications to ensure a good balance of workloads for the salesmen. It is known in the literature that the min-max MTSP is notoriously difficult to solve to optimality due to the poor lower bounds its linear relaxations provide. In this paper, we formulate two novel parametric variants of the MTSP called the "fair-MTSP". One variant is formulated as a Mixed-Integer Second Order Cone Program (MISOCP), and the other as a Mixed Integer Linear Program (MILP). Both focus on enforcing the workloads for the salesmen to be equitable, i.e., the distribution of tour lengths for the salesmen to be fair while minimizing the total cost of their tours. We present algorithms to solve the two variants of the fair-MTSP to global optimality and computational results on benchmark and real-world test instances that make a case for fair-MTSP as a viable alternative to the min-max MTSP., Comment: 10 pages

Scenarios seeking to address the issue of electroweak symmetry breaking often have heavy colored gauge bosons coupling preferentially to the top quark. Considering the bulk Randall-Sundrum as a typical example, we consider the prospects of the first Kaluza-Klein mode ($G^{(1)}$) of the gluon being produced at the LHC in association with a $t \bar{t}$ pair. The enhanced coupling not only dictates that the dominant decay mode would be to a $t \bar{t}$ pair, but also to a very large $G^{(1)}$ width, necessitating the use of a renormalised $G^{(1)}$ propagator. This, alongwith the presence of large backgrounds (specially $t \bar{t} j j$), renders a conventional cut-based analysis ineffective, yielding only marginal significances of only around 2$\sigma$. The use of Machine Learning (ML) techniques alleviates this problem to a great extent. In particular, the use of Artificial Neural Networks helps us identify the most discriminating observables, thereby allowing a significance in excess of 4$\sigma$ for $G^{(1)}$ masses of $\sim$ 4 TeV., Comment: 35 pages, 9 figures, 5 tables

In this work, we delve to investigate a feasible range of dark matter (DM) masses within a non-supersymmetric $SO(10)$ Grand Unified Theory (GUT) scalar dark matter model, in freeze-out scenario. This model includes a singlet scalar denoted as S and an inert doublet represented by $\phi$. Being part of SO(10), the quantum numbers of DM particles are assigned and hence we know their nature. These fields are odd under a discrete $Z_2$ matter parity $(-1)^{3(B-L)}$. The dark matter with mass 300 $\leq M_{DM} \leq$ 1000 GeV emerges as a mixture of the $Z_2$-odd scalar singlet $S$ and the neutral element of the doublet $\phi$, both residing within a \textbf{16}-dim scalar representation of $SO(10)$. In this work we consider a real scalar \textbf{S} belonging to \textbf{16} of SO(10) as DM. We also investigate the one-loop vacuum stability through the solution of Renormalization Group Equations (RGEs) for the model's parameters. Subsequently, we scrutinize the model's predictions within the confines of contemporary theoretical and experimental restrictions. In addition to achieving vacuum stability in the SO(10) framework, the DM mass is found to lie in the previously unaddressed (theoretically) intermediate mass region of 300$\leqslant$ MDM $\leqslant$ 1000 GeV which also adheres to many current phenomenological constraints, like recent direct experimental bounds from XENON1T, indirect detection bounds from Fermi-LAT experiment, Higgs invisible decay and Electroweak Precision Test. The stability of the electroweak vacuum is seen to be present up to the Planck scale. These model predictions possess the potential for future validation through dark matter search experiments, as they are testable in future DM search experiments, along with the added feature that the model is a part of an elegant grand unified theory., Comment: 17 pages, 6 figures, 1 table

In this work, a higher order compact (HOC) discretization is developed on the nonuniform polar grid. The discretization conceptualized using the unsteady convection-diffusion equation (CDE) is further extended to flow problems governed by the Navies-Stokes (N-S) equations as well as the Boussinesq equations. The scheme developed here combines the advantages of body-fitted mesh with grid clustering, thereby making it efficient to capture flow gradients on polar grids. The scheme carries a spatial convergence of order three with temporal order of convergence being almost two. Diverse flow problems are being investigated using the scheme. Apart from two verification studies we validate the scheme by time marching simulation for the benchmark problem of driven polar cavity and the problem of natural convection in the horizontal concentric annulus. In the process, a one-sided approximation for the Neumann boundary condition for vorticity is also presented. Finally, the benchmark problem of forced convection around a circular cylinder is tackled. The results obtained in this study are analyzed and compared with the well-established numerical and experimental data wherever available in the literature. The newly developed scheme is found to generate accurate solutions in each case.

Various quantum algorithms require usage of arbitrary diagonal operators as subroutines. For their execution on a physical hardware, those operators must be first decomposed into target device's native gateset and its qubit connectivity for entangling gates. Here, we assume that the allowed gates are exactly the CX gate and the parameterized phase gate. We introduce a framework for the analysis of CX-only circuits and through its lens provide solution constructions for several different device topologies (fully-connected, linear and circular). We also introduce two additional variants of the problem. Those variants can be used in place of exact decomposition of the diagonal operator when the circuit following it satisfies a set of prerequisites, enabling further reduction in the CX cost of implementation. Finally, we discuss how to exploit the framework for the decomposition of a particular, rather than general, diagonal operator., Comment: 17 pages, 12 figures, 1 table