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Diksha Gupta

Publications and source records attributed to Diksha Gupta.

At least 19 recordsLinked to original sources
arXiv2026

Cascading Impacts of the USA--China Trade War on Global Oilseed Supply Chain

Global supply chains are highly interconnected, making them vulnerable to cascading disruptions induced by trade policy shocks. Understanding how such disruptions propagate through production networks, and how mitigation mechanisms such as trade reallocation and production adjustment can alleviate their impacts, remains a central challenge. In this work, we develop a linear programming formulation of an Input-Output (IO) system that captures cascading supply-chain disruptions together with trade reallocation and production expansion. Our formulation yields a system-level equilibrium characterization that enables the joint analysis of disruption propagation and mitigation within a unified framework. We propose an efficient algorithm for computing approximate equilibrium solutions by minimizing total unmet demand in large IO systems. We apply our approach to tariff-induced disruptions in the global oilseeds supply chain arising from the U.S.-China trade war. Our results show that a localized 70% disruption to flows from the U.S. oilseeds sector to China leads to a 3.27% loss in global output, with China experiencing a disproportionate loss of 14.02%. As a counterfactual mitigation strategy, allowing a 20% reallocation from Brazil's oilseed sector to China significantly reduces global output losses to 1.36%, although pressure remains high on final-demand flows. We further investigate production expansion as an additional mitigation mechanism and show that it introduces tradeoffs between reducing global final-demand losses and protecting Brazil's domestic flows. Domestic reallocation disproportionately shifts losses toward smaller economies, while globally sourced expansion redistributes losses more broadly across the network.

econ.GN↗
arXiv2026

The isocritical regime for mixed local-nonlocal $(p,q)$ Laplacian: existence of ground state, and decay estimates

We study the mixed local-nonlocal operator $\mathcal{L}_{p,q} := -\Delta_p + (-\Delta)_q^s$ in the isocritical regime $p^* = q_s^*$, i.e. $1 - N/p = s - N/q$, under which both operators become critical for the same nonlinearity. We consider \[ -\Delta_p u + (-\Delta)_q^s u = |u|^{p^*-2}u \qquad \text{in } \mathbb{R}^N, \] with $N \geq 2$, $1 < p < N$, $0 < s < 1$, $1 < sq < N$. In this regime the energy space reduces to $\mathcal{D}_0^{1,p}(\mathbb{R}^N)$, and both best Sobolev constants enter the variational structure simultaneously. We prove: $(i)$ existence of a nonnegative radial ground state via Nehari manifold methods and a double-threshold concentration-compactness analysis; $(ii)$ a logarithmic energy estimate, weak comparison principle, and strong maximum principle for all admissible exponents; $(iii)$ a weak Harnack inequality; and $(iv)$ sharp two-sided decay $U(x) \asymp |x|^{-(N-p)/(p-1)}$ for positive radial solutions, matching the fundamental solution of the $p$-Laplacian.

math.AP↗
arXiv2026

Robust Network Flow Interdiction Problems with Applications to Counter-Narcotics

Interdiction problems arise in a number of application areas, including global security, supply chains, and critical infrastructure protection - the goal is inhibit the movement of goods, people or information. An area of particular interest is counter-narcotics, where nodes or edges in a network are placed under surveillance or blocked to minimize the flow of illicit drugs from source to the destination. A fundamental challenge in this narco-traffic interdiction is data scarcity: available datasets are limited by the very nature of the problem and provide only partial and uncertain views of trafficking networks. Thus, developing robust interdiction methods that take this inherent lack of information is critical. In this paper we initiate the study of network flow interdiction problems under network uncertainty. First, using a limited real-world dataset, we generate an ensemble of plausible network realizations representing alternative trafficking scenarios. The method combines simulations with mathematical programming techniques to generate network ensembles that are consistent with the observed data. Second, we formulate the robust network flow interdiction problem and develop an integer linear program to solve the problem. We evaluate the optimal interdiction strategy and obtain the residual flows over the scenarios. Our analysis reveals that even modest budgets can yield significant flow reductions. However, optimal solutions vary substantially across scenarios, motivating the need for robust solutions. We show that the robust strategy achieves near-optimal performance across all near-real world realizations while remaining stable under structural uncertainty. This simulation-driven approach provides a principled basis for policy analysis and supports maximizing the return on interdiction investments in uncertain, data-limited environments.

cs.CE↗
arXiv2026

Estimating the cascading global impacts of gas disruptions in Qatar

This study examines the global impacts of a localized disruption in Qatar's gas sector using a multi-regional input-output framework and scenario-based analysis. While the direct impacts of this disruption on importing countries are clear, indirect and cascading impacts are not well understood. We use a Multiregional input-output (MRIO) model to assess the impact of this disruption and to determine whether trade reallocations and increased production can mitigate its effects. Our analysis shows that this disruption leads to significant gas supply losses in Asia and Europe, with the largest aggregate impacts observed in India, China, and South Korea. Allowing for trade reallocation partially mitigates these losses. Further expansion of production capacity among major gas-producing countries improves supply conditions and leads to broader output gains; however, these benefits remain concentrated in a few large economies. Even significant increases in production among top producers offer limited relief to economies such as India and Pakistan. Overall, the results highlight the uneven distribution of both vulnerabilities and recovery potential within global supply chains. While adaptive mechanisms such as trade reallocation and production expansion can alleviate the effects of supply shocks, their effectiveness is limited and heterogeneous. The findings underscore the importance of network structure in shaping shock propagation and resilience, offering insights for managing systemic risks in an interconnected global economy.

physics.soc-ph↗
arXiv2025

Reconciling Communication Compression and Byzantine-Robustness in Distributed Learning

Distributed learning enables scalable model training over decentralized data, but remains hindered by Byzantine faults and high communication costs. While both challenges have been studied extensively in isolation, their interplay has received limited attention. Prior work has shown that naively combining communication compression with Byzantine-robust aggregation can severely weaken resilience to faulty nodes. The current state-of-the-art, Byz-DASHA-PAGE, leverages a momentum-based variance reduction scheme to counteract the negative effect of compression noise on Byzantine robustness. In this work, we introduce RoSDHB, a new algorithm that integrates classical Polyak momentum with a coordinated compression strategy. Theoretically, RoSDHB matches the convergence guarantees of Byz-DASHA-PAGE under the standard $(G,B)$-gradient dissimilarity model, while relying on milder assumptions and requiring less memory and communication per client. Empirically, RoSDHB demonstrates stronger robustness while achieving substantial communication savings compared to Byz-DASHA-PAGE.

cs.LG↗
arXiv2025

Elliptic Problems Involving Mixed Local-Nonlocal Operator in the Hyperbolic Space

This paper explores the existence of solutions to a class of nonlinear elliptic equations involving a mixed local-nonlocal operator of the form $-Δ_{\mathbb{B}^N} + (-Δ_{\mathbb{B}^N})^s$, with $0 < s < 1$, set in the hyperbolic space $\mathbb{B}^N$. By employing variational methods, we address both subcritical and critical nonlinearities, establishing the existence of weak solutions under appropriate conditions.

math.AP↗
arXiv2025

Global Compactness Result for a Brézis-Nirenberg-Type Problem Involving Mixed Local Nonlocal Operator

This paper investigates the profile decomposition of Palais-Smale sequences associated with a Brezis-Nirenberg type problem involving a combination of mixed local nonlocal operators, given by \begin{equation*} \left\{\begin{aligned} &-Δu + (-Δ)^s u - λu = |u|^{2^*-2}u \;\;\mbox{ in } Ω, &\quad u=0\,\mbox{ in }\mathbb{R}^N\setminus Ω. \end{aligned} \right. \end{equation*} where $Ω\subseteq \mathbb{R}^{N}$ is a smooth bounded domain with $N \geq 3$, $s\in (0,1),\,λ\in\mathbb{R}$ is a real parameter and $2^* = \frac{2N}{N - 2} $ denotes the critical Sobolev exponent. As an application of the derived global compactness result, we further study the existence of positive solution of the corresponding Coron-type problem (C. R. Acad. Sci. Paris Sér I Math, 299(7):209-212, 1984) when $λ=0$.

math.AP↗
arXiv2024

Poincaré-Sobolev equations with the critical exponent and a potential in the hyperbolic space

On the hyperbolic space, we study a semilinear equation with non-autonomous nonlinearity having a critical Sobolev exponent. The Poincaré-Sobolev equation on the hyperbolic space explored by Mancini and Sandeep [Ann. Sc. Norm. Super. Pisa Cl. Sci. 7 (2008)] resembles our equation. As seen from the profile decomposition of the energy functional associated with the problem, the concentration happens along two distinct profiles: localised Aubin-Talenti bubbles and hyperbolic bubbles. Standard variational arguments cannot obtain solutions because of nontrivial potential and concentration phenomena. As a result, a deformation-type argument based on the critical points at infinity of the associated variational problem has been carried out to obtain solution for $N>6.$ Conformal change of metric is used for proofs, enabling us to convert the original equation into a singular equation in a ball in $\mathbb{R}^N$ and perform a fine blow-up analysis.

math.AP↗
arXiv2024

Existence, symmetry and regularity of ground states of a non linear choquard equation in the hyperbolic space

In this paper, we explore the positive solutions of the following nonlinear Choquard equation involving the green kernel of the fractional operator $(-Δ_{\mathbb{B}^N})^{-α/2}$ in the hyperbolic space \begin{equation} \begin{aligned} -Δ_{\mathbb{B}^{N}} u \, - \, λu \, &= \left[(- Δ_{\mathbb{B}^{N}})^{-\fracα{2}}|u|^p\right]|u|^{p-2}u, \end{aligned} \end{equation} where $Δ_{\mathbb{B}^{N}}$ denotes the Laplace-Beltrami operator on $\mathbb{B}^{N}$, $λ\leq \frac{(N-1)^2}{4}$, $1 < p < 2^*_α = \frac{N+α}{N-2}$, $0 < α< N$, $N \geq 3$, $2^*_α$ is the critical exponent in the context of the Hardy-Littlewood-Sobolev inequality. This study is analogous to the Choquard equation in the Euclidean space, which involves the non-local Riesz potential operator. We consider the functional setting within the Sobolev space $H^1(\mathbb{B}^N)$, employing advanced harmonic analysis techniques, particularly the Helgason Fourier transform and semigroup approach to fractional Laplacian. Moreover, the Hardy-Littlewood-Sobolev inequality on complete Riemannian manifolds, as developed by Varopoulos, is pivotal in our analysis. We prove an existence result for the above problem in the subcritical case. Moreover, we also demonstrate that solutions exhibit radial symmetry, and establish the regularity properties.

math.AP↗
arXiv2024

A study on fuzzy plane and its application on fuzzy plane fitting

In this paper, I obtain an $S$-type fuzzy point when two fuzzy numbers for two independent variables and a corresponding fuzzy number for the dependent variable are given. A comprehensive study on a conceptualization of a fuzzy plane as a collection of fuzzy numbers, or fuzzy points is proposed. A perpendicular fuzzy distance from a fuzzy point to a fuzzy plane is also revisited. An application of the proposed fuzzy plane is made to fit a fuzzy plane to the available data sets of imprecise locations in $\mathbb{R}^3$. Moreover, a degree of fuzzily fitted fuzzy plane to the given data sets of fuzzy points is defined. All the fuzzy geometric construction and characteristics of fuzzy planes are explored with the help of same and inverse points ideas. All the study is supported by numerical examples and illustrated by fuzzy geometrical figures. This study provides a framework for developing a fuzzy plane-fitting model that will benefit the fields of curve detecting and fitting, image processing for industrial and scientific applications, signal processing, and problems of shape recognition.

math.GM↗
arXiv2023

Global compactness result and multiplicity of solutions for a class of critical exponent problem in the hyperbolic space

This paper deals with the global compactness and multiplicity of positive solutions to problems of the type $$ -Δ_{\mathbb B^N} u -λu=a(x) |u|^{2^*-2}u+f(x) \quad\text{in } \mathbb B^N, \quad u\in H^1(\mathbb B^N),$$ where $\mathbb B^N$ denotes the ball model of the hyperbolic space of dimension $N\geq 4$, $2^*=\frac{2N}{N-2}$, $\frac{N(N-2)}{4}<λ<\frac{(N-1)^2}{4}$ and $f\in H^{-1}(\mathbb B^N)$ ($f\not\equiv 0$) is a non-negative functional in the dual space of $H^1(\mathbb B^N)$. The potential $a\in L^\infty(\mathbb B^N)$ is assumed to be strictly positive, such that $\lim_{ d(x,0)\to \infty}a(x)=1$, where $d(x,0)$ denotes the geodesic distance. We establish profile decomposition of the associated functional. We show that concentration takes place along two different profiles, namely along hyperbolic bubbles and localized Aubin-Talenti bubbles. For $f=0$ and $a\equiv 1$, profile decomposition was studied by Bhakta and Sandeep [Calc. Var. PDE, 2012]. However, due to the presence of $a(.)$, an extension of profile decomposition to the present set-up is highly nontrivial and requires several delicate estimates and geometric arguments concerning the isometry group (Möbius group) of the hyperbolic space. Further, using the decomposition result, we derive various energy estimates involving the interacting hyperbolic bubbles and hyperbolic bubbles with localized Aubin-Talenti bubbles. Finally, combining these estimates with topological and variational arguments, we establish a multiplicity of positive solutions in the cases: $a\geq 1$ and $a<1$ separately. The equation studied in this article can be thought of as a variant of a scalar-field equation with a critical exponent in the hyperbolic space, although such a critical exponent problem in the Euclidean space $\mathbb{R}^N$ has only a trivial solution when $f \equiv 0,$ $a(x)\equiv1$ and $λ< 0.$

math.AP↗
arXiv2023

On a class of elliptic equations with Critical Perturbations in the hyperbolic space

We study the existence and non-existence of positive solutions for the following class of nonlinear elliptic problems in the hyperbolic space $$ -Δ_{\mathbb{B}^N} u-λu=a(x)u^{p-1} \, + \, \varepsilon u^{2^*-1} \,\;\;\text{in}\;\mathbb{B}^{N}, \quad u \in H^{1}{(\mathbb{B}^{N})}, $$ where $\mathbb{B}^N$ denotes the hyperbolic space, $2<p<2^*:=\frac{2N}{N-2}$, if $N \geqslant 3; 2<p<+\infty$, if $N = 2,\;λ< \frac{(N-1)^2}{4}$, and $0< a\in L^\infty(\mathbb{B}^N).$ We first prove the existence of a positive radially symmetric ground-state solution for $a(x) \equiv 1.$ Next, we prove that for $a(x) \geq 1$, there exists a ground-state solution for $\varepsilon$ small. For proof, we employ ``conformal change of metric" which allows us to transform the original equation into a singular equation in a ball in $\mathbb R^N$. Then by carefully analysing the energy level using blow-up arguments, we prove the existence of a ground-state solution. Finally, the case $a(x) \leq 1$ is considered where we first show that there is no ground-state solution, and prove the existence of a \it bound-state solution \rm (high energy solution) for $\varepsilon$ small. We employ variational arguments in the spirit of Bahri-Li to prove the existence of high energy-bound-state solutions in the hyperbolic space.

math.AP↗
arXiv2023

Bankrupting Sybil Despite Churn

A Sybil attack occurs when an adversary controls multiple identifiers (IDs) in a system. Limiting the number of Sybil (bad) IDs to a minority is critical to the use of well-established tools for tolerating malicious behavior, such as Byzantine agreement and secure multiparty computation. A popular technique for enforcing a Sybil minority is resource burning: the verifiable consumption of a network resource, such as computational power, bandwidth, or memory. Unfortunately, typical defenses based on resource burning require non-Sybil (good) IDs to consume at least as many resources as the adversary. Additionally, they have a high resource burning cost, even when the system membership is relatively stable. Here, we present a new Sybil defense, ERGO, that guarantees (1) there is always a minority of bad IDs; and (2) when the system is under significant attack, the good IDs consume asymptotically less resources than the bad. In particular, for churn rate that can vary exponentially, the resource burning rate for good IDs under ERGO is O(\sqrt{TJ} + J), where T is the resource burning rate of the adversary, and J is the join rate of good IDs. We show this resource burning rate is asymptotically optimal for a large class of algorithms. We empirically evaluate ERGO alongside prior Sybil defenses. Additionally, we show that ERGO can be combined with machine learning techniques for classifying Sybil IDs, while preserving its theoretical guarantees. Based on our experiments comparing ERGO with two previous Sybil defenses, ERGO improves on the amount of resource burning relative to the adversary by up to 2 orders of magnitude without machine learning, and up to 3 orders of magnitude using machine learning.

cs.CR↗
arXiv2022

Multiplicity of positive solutions for a class of nonhomogeneous elliptic equations in the hyperbolic space

The paper is concerned with positive solutions to problems of the type \begin{equation*} -\Delta_{\mathbb{B}^N} u - \lambda u = a(x) |u|^{p-1}\;u \, + \, f \, \;\;\text{in}\;\mathbb{B}^{N}, \quad u \in H^{1}{(\mathbb{B}^{N})}, \end{equation*} where $\mathbb{B}^N$ denotes the hyperbolic space, $1 0.$ Subsequently, we establish the existence of two positive solutions for $a(x) \equiv 1$ and prove asymptotic estimates for positive solutions using barrier-type arguments. The proofs for existence combine variational arguments, key energy estimates involving hyperbolic bubbles.

math.AP↗
arXiv2022

Existence of high energy positive solutions for a class of elliptic equations in the hyperbolic space

We study the existence of positive solutions for the following class of scalar field problem on the hyperbolic space $$ -Δ_{\mathbb{H}^N} u - λu = a(x) |u|^{p-1} \, u\;\;\text{in}\;\mathbb{B}^{N}, \quad u \in H^{1}{(\mathbb{B}^{N})}, $$ where $\mathbb{B}^N$ denotes the hyperbolic space, $1<p<2^*-1:=\frac{N+2}{N-2}$, if $N \geqslant 3; 1<p<+\infty$, if $N = 2,\;λ< \frac{(N-1)^2}{4}$, and $0< a\in L^\infty(\mathbb{B}^N).$ We prove the existence of a positive solution by introducing the min-max procedure in the spirit of Bahri-Li in the hyperbolic space and using a series of new estimates involving interacting hyperbolic bubbles.

math.AP↗
arXiv2022

Limitations of a proposed correction for slow drifts in decision criterion

Trial history biases in decision-making tasks are thought to reflect systematic updates of decision variables, therefore their precise nature informs conclusions about underlying heuristic strategies and learning processes. However, random drifts in decision variables can corrupt this inference by mimicking the signatures of systematic updates. Hence, identifying the trial-by-trial evolution of decision variables requires methods that can robustly account for such drifts. Recent studies (Lak'20, Mendonça'20) have made important advances in this direction, by proposing a convenient method to correct for the influence of slow drifts in decision criterion, a key decision variable. Here we apply this correction to a variety of updating scenarios, and evaluate its performance. We show that the correction fails for a wide range of commonly assumed systematic updating strategies, distorting one's inference away from the veridical strategies towards a narrow subset. To address these limitations, we propose a model-based approach for disambiguating systematic updates from random drifts, and demonstrate its success on real and synthetic datasets. We show that this approach accurately recovers the latent trajectory of drifts in decision criterion as well as the generative systematic updates from simulated data. Our results offer recommendations for methods to account for the interactions between history biases and slow drifts, and highlight the advantages of incorporating assumptions about the generative process directly into models of decision-making.

q-bio.NC↗
arXiv2020

Resource Burning for Permissionless Systems

Proof-of-work puzzles and CAPTCHAS consume enormous amounts of energy and time. These techniques are examples of resource burning: verifiable consumption of resources solely to convey information. Can these costs be eliminated? It seems unlikely since resource burning shares similarities with "money burning" and "costly signaling", which are foundational to game theory, biology, and economics. Can these costs be reduced? Yes, research shows we can significantly lower the asymptotic costs of resource burning in many different settings. In this paper, we survey the literature on resource burning; take positions based on predictions of how the tool is likely to evolve; and propose several open problems targeted at the theoretical distributed-computing research community.

cs.DC↗
arXiv2020

ToGCom: An Asymmetric Sybil Defense

Proof-of-work (PoW) is one of the most common techniques to defend against Sybil attacks. Unfortunately, current PoW defenses have two main drawbacks. First, they require work to be done even in the absence of an attack. Second, during an attack, they require good identities (IDs) to spend as much as the attacker. Recent theoretical work by Gupta, Saia, and Young suggests the possibility of overcoming these two drawbacks. In particular, they describe a new algorithm, GMCom, that always ensures that a minority of IDs are Sybil. They show that rate at which all good IDs perform computation is $O(J_G + \sqrt{T(J_G+1)})$, where $J_G$ is the join rate of good IDs, and $T$ is the rate at which the adversary performs computation. Unfortunately, this cost bound only holds in the case where (1) GMCom always knows the join rate of good IDs; and (2) there is a fixed constant amount of time that separates join events by good IDs. Here, we present ToGCom, which removes these two shortcomings. To do so, we design and analyze a mechanism for estimating the join rate of good IDs; and also devise a new method for setting the computational cost to join the system. Additionally, we evaluate the performance of ToGCom alongside prior PoW-based defenses. Based on our experiments, we design heuristics that further improve the performance of ToGCom by up to $3$ orders of magnitude over these previous Sybil defenses.

cs.DC↗