Department of MathematicsNo Descriptionhttps://hdl.handle.net/11693/136912024-02-28T04:00:41Z2024-02-28T04:00:41Z7131The forcing effect on the evolution of certainty in a small decision making group by consensus Gheondea-Eladi, Alexandra Gheondea, Aurelianhttps://hdl.handle.net/11693/1141852024-02-02T00:07:18Z2024-02-01T00:00:00Zdc.title: The forcing effect on the evolution of certainty in a small decision making group by consensus
dc.contributor.author: Gheondea-Eladi, Alexandra ; Gheondea, Aurelian
2024-02-01T00:00:00ZErratum: On the extremal points of the Λ-Polytopes and classical simulatıon of quantum computation with magic statesCihan, OkayZurel, MichaelRaussendorf, Roberthttps://hdl.handle.net/11693/1120572023-03-06T08:04:08Z2022-05-01T00:00:00Zdc.title: Erratum: On the extremal points of the Λ-Polytopes and classical simulatıon of quantum computation with magic states
dc.contributor.author: Cihan, Okay; Zurel, Michael; Raussendorf, Robert
dc.description.abstract: We will fix an error in the proof of Theorem 2 of the work On the extremal points of the $\Lambda $-polytopes and classical simulation of quantum computation with magic states by the current authors, published in Quantum Information and Computation Vol.21 No.13\&14, 1533-7146 (2021). The theorem as it is stated is still correct, however there is a gap in the proof that needs to be filled.
2022-05-01T00:00:00ZTritangents to smooth sextic curvesDegtyarev, Alexhttps://hdl.handle.net/11693/1120292023-03-03T00:07:22Z2022-10-21T00:00:00Zdc.title: Tritangents to smooth sextic curves
dc.contributor.author: Degtyarev, Alex
dc.description.abstract: We prove that a smooth plane sextic curve can have at most 72 tritangents, whereas a smooth real sextic may have at most 66 real tritangents. © 2022 Association des Annales de l'Institut Fourier. All rights reserved.
2022-10-21T00:00:00ZOptimizing foreign exchange reserves: Protection against external shocks in GhanaAbdul-Rahaman, Abdul-RashidHongxing, YaoAlhassan Alolo Akeji, Abdul-RasheedAyamba, Emmanuel CaesarBernard Pea-Assounga, Jean BaptisteAlhassan, Mohammed Kamilhttps://hdl.handle.net/11693/1120162023-03-03T00:07:41Z2022-11-02T00:00:00Zdc.title: Optimizing foreign exchange reserves: Protection against external shocks in Ghana
dc.contributor.author: Abdul-Rahaman, Abdul-Rashid; Hongxing, Yao; Alhassan Alolo Akeji, Abdul-Rasheed; Ayamba, Emmanuel Caesar; Bernard Pea-Assounga, Jean Baptiste; Alhassan, Mohammed Kamil
dc.description.abstract: Using Least Square Residual Minimization techniques, this paper develops an optimal reserve model, known as the OPREM model, which is essential in optimizing the costs of reserve holding. The paper also sets-out to test and compare the relative predictions of economic trends of the OPREM model as well as the predictions of alternative models in literature. Establishing the predictive accuracy of economic trends of these models are crucial for the gradual and cost-effective accumulation of reserves. The research concludes that, the decision to optimize the cost of reserves under a stable currency environment is reliant on the gold impact factor and not on inflation or interest rates. We also found on further analysis of the OPREM that the OPREM model is better positioned to eliminate the procyclicality and perverse rush in reserve build-ups experienced in developing and emerging countries by effectively setting the reserve stock against economic trends. The research fixes the optimal reserves around a benchmark of 0.7–1.2 of previous year's optimal value. However, in the absence of past optimal values, a benchmark between 2 and 6 times of average inflows for short-term analysis or analysis with small data observations. However, for long-term analysis or analysis with large data frequency (i.e., exceeding 13 data observations), the reserve stock should be fixed on a benchmark of 2–9 times of the average inflows. Copyright © 2022 Abdul-Rahaman, Hongxing, Alhassan Alolo Akeji, Ayamba, Bernard Pea-Assounga and Alhassan.
2022-11-02T00:00:00ZDispersion estimates for the boundary integral operator associated with the fourth order Schrödinger equation posed on the half lineÖzsarı, TürkerAlkan, KıvılcımKalimeris, Konstantinoshttps://hdl.handle.net/11693/1119122023-03-01T00:08:38Z2021-09-01T00:00:00Zdc.title: Dispersion estimates for the boundary integral operator associated with the fourth order Schrödinger equation posed on the half line
dc.contributor.author: Özsarı, Türker; Alkan, Kıvılcım; Kalimeris, Konstantinos
dc.description.abstract: In this paper, we prove dispersion estimates for the boundary integral operator associated with the fourth order Schr¨odinger equation posed on the half line. Proofs of such estimates for domains with boundaries are rare and generally require highly technical approaches, as opposed to our simple treatment which is based on constructing a boundary integral operator of oscillatory nature via the Fokas method. Our method is uniform and can be extended to other higher order partial differential equations where the main equation possibly involves more than one spatial derivatives.
2021-09-01T00:00:00ZGeometry of information structures, strategic measures and associated stochastic control topologiesSaldı, NaciYüksel, Serdarhttps://hdl.handle.net/11693/1118722023-03-01T00:01:20Z2022-01-01T00:00:00Zdc.title: Geometry of information structures, strategic measures and associated stochastic control topologies
dc.contributor.author: Saldı, Naci; Yüksel, Serdar
dc.description.abstract: In many areas of applied mathematics, decentralization of information is a ubiquitous attribute affecting how to approach a stochastic optimization, decision and estimation, or control problem. In this review article, we present a general formulation of information structures under a probability theoretic and geometric formulation. We define information structures, place various topologies on them, and study closedness, compactness and convexity properties on the strategic measures induced by information structures and decentralized control/decision policies under varying degrees of relaxations with regard to access to private or common randomness. Ultimately, we present existence and tight approximation results for optimal decision/control policies. We discuss various lower bounding techniques, through relaxations and convex programs ranging from classically realizable and classically non-realizable (such as quantum theoretic and non-signaling) relaxations. For each of these, we establish closedness and convexity properties and also a hierarchy of correlation structures. As a further theme, we review and introduce various topologies on decision/ control strategies defined independent of information structures, but for which information structures determine whether the topologies entail utility in arriving at existence, compactness, convexification or approximation results. These approaches, which we term as the strategic measures approach and the control topology approach, lead to complementary results on existence, approximations and upper and lower bounds in optimal decentralized stochastic decision, estimation, and control problems © 2022. Probability Surveys.All Rights Reserved.
2022-01-01T00:00:00ZThe interior-boundary Strichartz estimate for the Schrödinger equation on the half-line revisitedKöksal, BilgeÖzsarı, Türkerhttps://hdl.handle.net/11693/1118412023-02-28T00:08:54Z2022-01-01T00:00:00Zdc.title: The interior-boundary Strichartz estimate for the Schrödinger equation on the half-line revisited
dc.contributor.author: Köksal, Bilge; Özsarı, Türker
dc.description.abstract: In recent papers, it was shown for the biharmonic Schrödinger equation and 2D Schrödinger equation that Fokas method-based formulas are capable of defining weak solutions of associated nonlinear initial boundary value problems (ibvps) below the Banach algebra threshold. In view of these results, we revisit the theory of interiorboundary Strichartz estimates for the Schrödinger equation posed on the right half line, considering both Dirichlet and Neumann cases. Finally, we apply these estimates to obtain low regularity solutions for the nonlinear Schrödinger equation (NLS) with Neumann boundary condition and a coupled system of NLS equations defined on the half line with Dirichlet/Neumann boundary conditions. © This work is licensed under a Creative Commons Attribution 4.0 International License.
2022-01-01T00:00:00Z800 conics on a smooth quartic surfaceDegtyarev, Alexhttps://hdl.handle.net/11693/1118202023-02-28T00:09:01Z2022-03-10T00:00:00Zdc.title: 800 conics on a smooth quartic surface
dc.contributor.author: Degtyarev, Alex
dc.description.abstract: We construct an example of a smooth spatial quartic surface that contains 800 irreducible conics. © 2022 Elsevier B.V.
2022-03-10T00:00:00ZOptimality of independently randomized symmetric policies for exchangeable stochastic teams with infinitely many decision makersSanjari, S.Saldi, NaciYüksel, S.https://hdl.handle.net/11693/1118132023-02-28T00:07:30Z2022-08-24T00:00:00Zdc.title: Optimality of independently randomized symmetric policies for exchangeable stochastic teams with infinitely many decision makers
dc.contributor.author: Sanjari, S.; Saldi, Naci; Yüksel, S.
dc.description: We study stochastic teams (known also as decentralized stochastic control problems or identical interest stochastic dynamic games) with large or countably infinite numbers of decision makers and characterize the existence and structural properties of (globally) optimal policies. We consider both static and dynamic nonconvex teams where the cost function and dynamics satisfy an exchangeability condition. To arrive at existence and structural results for optimal policies, we first introduce a topology on control policies, which involves various relaxations given the decentralized information structure. This is then utilized to arrive at a de Finetti–type representation theorem for exchangeable policies. This leads to a representation theorem for policies that admit an infinite exchangeability condition. For a general setup of stochastic team problems with N decision makers, under exchangeability of observations of decision makers and the cost function, we show that, without loss of global optimality, the search for optimal policies can be restricted to those that are N-exchangeable. Then, by extending N-exchangeable policies to infinitely exchangeable ones, establishing a convergence argument for the induced costs, and using the presented de Finetti–type theorem, we establish the existence of an optimal decentralized policy for static and dynamic teams with countably infinite numbers of decision makers, which turns out to be symmetric (i.e., identical) and randomized. In particular, unlike in prior work, convexity of the cost in policies is not assumed. Finally, we show the near optimality of symmetric independently randomized policies for finite N-decision-maker teams and thus establish approximation results for N-decision-maker weakly coupled stochastic teams.
2022-08-24T00:00:00ZConjectural invariance with respect to the fusion system of an almost-source algebraBarker, LaurenceGelvin, Matthewhttps://hdl.handle.net/11693/1117892023-02-28T00:07:04Z2022-03-23T00:00:00Zdc.title: Conjectural invariance with respect to the fusion system of an almost-source algebra
dc.contributor.author: Barker, Laurence; Gelvin, Matthew
dc.description.abstract: We show that, given an almost-source algebra 𝐴 of a 𝑝-block of a finite group 𝐺, then the unit group of 𝐴 contains a basis stabilized by the left and right multiplicative action of the defect group if and only if, in a sense to be made precise, certain relative multiplicities of local pointed groups are invariant with respect to the fusion system. We also show that, when 𝐺 is 𝑝-solvable, those two equivalent conditions hold for some almost-source algebra of the given 𝑝-block. One motive lies in the fact that, by a theorem of Linckelmann, if the two equivalent conditions hold for 𝐴, then any stable basis for 𝐴 is semicharacteristic for the fusion system.
2022-03-23T00:00:00Z