arXiv subjects

Jacob Turner

Publications and source records attributed to Jacob Turner.

16 recordsLinked to original sources

arXiv2026

Energy Transfer Mechanisms in Wake-Modulated Transonic Flutter

Transonic flutter is a detrimental aeroelastic instability that can generate large-amplitude structural oscillations, leading to severe vibration, fatigue damage, reduced operational limits, and potentially catastrophic structural failure. Incoming wake disturbances can further amplify this instability, making it critical to identify the underlying aerodynamic mechanisms responsible for predicting and controlling flutter onset. The underlying flow physics is complex with nonlinear interactions between the wake and the wing, shock motion, shock-induced flow separation, vortex shedding and the wing motion. In this study, we perform high-fidelity direct numerical simulations of a sinusoidally pitching NACA0012 airfoil with an underwing cylinder at various transonic Mach numbers and a Reynolds number of 10,000. Through energy maps, we identify that the addition of the cylinder significantly expands flutter boundaries compared to an airfoil-only system. We extend the force partitioning method to partition the power transferred between the flow and the airfoil for compressible flows. Application of this approach to distinct regions of the flow domain indicates that the gap flow between the wing and the cylinder is the dominant contributor to the energy transfer from flow to the wing. The blockage effects due to the cylinder cause flow acceleration on the wing which further enhances the tendency for flutter. We investigate cylinder placement relative to the airfoil to reveal that flutter is enhanced only when the cylinder is placed upstream of the pivot point on the airfoil. The current study highlights how such partitioning methods can parse force and energy transfer mechanisms in complex, unsteady high-speed flows.

physics.flu-dyn↗

arXiv2025

Inferring Mbh-Mbulge Evolution from the Gravitational Wave Background

We test the impact of an evolving supermassive black hole (SMBH) mass scaling relation (Mbh-Mbulge) on the predictions for the gravitational wave background (GWB). The observed GWB amplitude is 2-3 times higher than predicted by astrophysically informed models which suggests the need to revise the assumptions in those models. We compare a semi-analytic model's ability to reproduce the observed GWB spectrum with a static versus evolving-amplitude Mbh-Mbulge relation. We additionally consider the influence of the choice of galaxy stellar mass function on the modeled GWB spectra. Our models are able to reproduce the GWB amplitude with either a large number density of massive galaxies or a positively evolving Mbh-Mbulge amplitude (i.e., the Mbh / Mbulge ratio was higher in the past). If we assume that the Mbh-Mbulge amplitude does not evolve, our models require a galaxy stellar mass function that implies an undetected population of massive galaxies (Mstellar > 10^11 Msun at z > 1). When the Mbh-Mbulge amplitude is allowed to evolve, we can model the GWB spectrum with all fiducial values and an Mbh-Mbulge amplitude that evolves as alpha(z) = alpha_0 (1 + z)^(1.04 +/- 0.5).

astro-ph.HE↗

arXiv2025

Layered Dirichlet Modeling to Assess the Changing Contributions of MLB Players as they Age

The productive career of a professional athlete is limited compared to the normal human lifespan. Most professional athletes have retired by age 40. The early retirement age is due to a combination of age-related performance and life considerations. While younger players typically are stronger and faster than their older teammates, older teammates add value to a team due to their experience and perspective. Indeed, the highest--paid major league baseball players are those over the age of 35. These players contribute intangibly to a team through mentorship of younger players; however, their peak athletic performance has likely passed. Given this, it is of interest to learn how more mature players contribute to a team in measurable ways. We examine the distribution of plate appearance outcomes from three different age groups as compositional data, using Layered Dirichlet Modeling (LDM). We develop a hypothesis testing framework to compare the average proportions of outcomes for each component among 3 of more groups. LDM can not only determine evidence for differences among populations, but also pinpoint within which component the largest changes are likely to occur. This framework can determine where players can be of most use as they age.

stat.ME↗

arXiv2020

Mapping Matchings to Minimum Vertex Covers: K\H{o}nig's Theorem Revisited

It is a celebrated result in early combinatorics that, in bipartite graphs, the size of maximum matching is equal to the size of a minimum vertex cover. K\H{o}nig's proof of this fact gave an algorithm for finding a minimum vertex cover from a maximum matching. In this paper, we revisit the connection this algorithm induces between the two types of structures. We find that all minimum vertex covers can be found by applying this algorithm to some matching and then classify which matchings give minimum vertex covers when this algorithm is applied to them.

math.CO↗

arXiv2019

Combining the Connection Scan Algorithm with Contraction Hierarchies

Since the first solutions finding minimally weighted routes in weighted digraphs, a plethora of literature has appeared improving the performance of shortest-path queries for use in real-world applications. In this paper, we detail how an advanced pre-processing technique for routing algorithms (which create objects known as Contraction Hierarchies) may be combined with the connection scan algorithm, an algorithm originally designed to work with public transportation networks using time tables. This provides an improvement over bi-directional Dijkstra or A${}^*$ search on Contraction Hierarchies.

cs.DS↗

arXiv2018

A New Optimization Layer for Real-Time Bidding Advertising Campaigns

While it is relatively easy to start an online advertising campaign, obtaining a high Key Performance Indicator (KPI) can be challenging. A large body of work on this subject has already been performed and platforms known as DSPs are available on the market that deal with such an optimization. From the advertiser's point of view, each DSP is a different black box, with its pros and cons, that needs to be configured. In order to take advantage of the pros of every DSP, advertisers are well-advised to use a combination of them when setting up their campaigns. In this paper, we propose an algorithm for advertisers to add an optimization layer on top of DSPs. The algorithm we introduce, called SKOTT, maximizes the chosen KPI by optimally configuring the DSPs and putting them in competition with each other. SKOTT is a highly specialized iterative algorithm loosely based on gradient descent that is made up of three independent sub-routines, each dealing with a different problem: partitioning the budget, setting the desired average bid, and preventing under-delivery. In particular, one of the novelties of our approach lies in our taking the perspective of the advertisers rather than the DSPs. Synthetic market data is used to evaluate the efficiency of SKOTT against other state-of-the-art approaches adapted from similar problems. The results illustrate the benefits of our proposals, which greatly outperforms the other methods.

cs.GT↗

arXiv2017

A new degree bound for local unitary and $n$-qubit SLOCC Invariants

Deep connections between invariant theory and entanglement have been known for some time and been the object of intense study. This includes the study of local unitary equivalence of density operators as well as entanglement that can be observed in stochastic local operations assisted by classical communication (SLOCC). An important aspect of both of these areas is the computation of complete sets of invariants polynomials. For local unitary equivalence as well as $n$-qubit SLOCC invariants, complete descriptions of these invariants exist. However, these descriptions give infinite sets; of great interest is finding generating sets of invariants. In this regard, degree bounds are highly sought after to limit the possible sizes of such generating sets. In this paper we give new upper bounds on the degrees of the invariants, both for a certain complete set of local unitary invariants as well as the $n$-qubit SLOCC invariants. We show that there exists a complete set of local unitary invariants of density operators in a Hilbert space $\mathcal{H}$, of dimension $d$, which are generated by invariants of degree at most $d^4$. This in turn allows us to show that the $n$-qubit SLOCC invariants are generated by invariants of degree at most $2^{4n}$.

quant-ph↗

arXiv2017

A Finite-Tame-Wild Trichotomy Theorem for Tensor Diagrams

In this paper, we consider the problem of determining when two tensor networks are equivalent under a heterogeneous change of basis. In particular, to a string diagram in a certain monoidal category (which we call tensor diagrams), we formulate an associated abelian category of representations. Each representation corresponds to a tensor network on that diagram. We then classify which tensor diagrams give rise to categories that are finite, tame, or wild in the traditional sense of representation theory. For those tensor diagrams of finite and tame type, we classify the indecomposable representations. Our main result is that a tensor diagram is wild if and only if it contains a vertex of degree at least three. Otherwise, it is of tame or finite type.

math.RT↗

arXiv2017

Topological classification of time-asymmetry in unitary quantum processes

Understanding which physical processes are symmetric with respect to time inversion is a ubiquitous problem in physics. In quantum physics, effective gauge fields allow emulation of matter under strong magnetic fields, realizing the Harper-Hofstadter, the Haldane models, demonstrating one-way waveguides and topologically protected edge states. Central to these discoveries is the chirality induced by time-symmetry breaking. In quantum walk algorithms, recent work has discovered implications time-reversal symmetry breaking has on the transport of quantum states which has enabled a host of new experimental implementations. We provide a full topological classification of the Hamiltonians of operators breaking time-reversal symmetry in their induced transition probabilities between elements in a preferred site-basis. We prove that a quantum process is necessarily time-symmetric for any choice of time-independent Hamiltonian precisely when the underlying support graph is bipartite or no Aharonov-Bohm phases are present in the gauge field. We further prove that certain bipartite graphs exhibit transition probability suppression, but not broken time-reversal symmetry. Furthermore, our development of a general framework characterizes gauge potentials on combinatorial graphs. These results and techniques fill an important missing gap in understanding the role this omnipresent effect has in quantum information and computation.

quant-ph↗

arXiv2016

Enumerative Aspects of Nullstellensatz Certificates

Using polynomial equations to model combinatorial problems has been a popular tool both in computational combinatorics as well as an approach to proving new theorems. In this paper, we look at several combinatorics problems modeled by systems of polynomial equations satisfying special properties. If the equations are infeasible, Hilbert's Nullstellensatz gives a certificate of this fact. These certificates have been studied and exhibit combinatorial meaning. In this paper, we generalize some known results and show that the Nullstellensatz certificate can be viewed as enumerating combinatorial structures. As such, Gr\"obner basis algorithms for solving these decision problems may implicitly be solving the enumeration problem as well.

math.CO↗

arXiv2016

On Subtilings of Polyomino Tilings

We consider a problem concerning tilings of rectangular regions by a finite library of polyominoes. We specifically look at rectangular regions of dimension $n\times m$ and ask whether or not a tiling of this region can be rearranged so that tiling of the $n\times m$ rectangle can be realized as a tiling of an $n\times m'$ rectangle and an $n\times m"$ rectangle, $m=m'+m"$. We call this a subtiling. We show that the associated decision problem is $\mathsf{NP}$-complete when restricted to rectangular polyominoes. We also show that for certain finite libraries of polyominoes, if $m$ is sufficiently large, a subtiling always exists and give bounds.

math.CO↗

arXiv2015

Tensors Masquerading as Matchgates: Relaxing Planarity Restrictions on Pfaffian Circuits

Holographic algorithms, alternatively known as Pfaffian circuits, have received a great deal of attention for giving polynomial-time algorithms of $\#\mathsf{P}$-hard problems. Much work has been done to determine the extent of what this machinery can do and the expressiveness of these circuits. One aspect of interest is the fact that these circuits must be planar. Work has been done to try and relax the planarity conditions and extend these algorithms further. We show that an approach based on orbit closures does not work, but give a different technique for allowing the SWAP gate to be used in a Pfaffian circuit given a suitable basis and restricted type of graph. This is done by exploiting the fact that the set of Pfaffian (co)gates always lies in a hyperplane. We then give a variety of bases that can be chosen such that the SWAP gate acts like a Pfaffian cogate and discuss how many SWAP gates can be implemented in a Pfaffian circuit.

math.AG↗

arXiv2015

A Complete Set of Invariants for LU-Equivalence of Density Operators

We show that two density operators of mixed quantum states are in the same local unitary orbit if and only if they agree on polynomial invariants in a certain Noetherian ring for which degree bounds are known in the literature. This implicitly gives a finite complete set of invariants for local unitary equivalence. This is done by showing that local unitary equivalence of density operators is equivalent to local ${\rm GL}$ equivalence and then using techniques from algebraic geometry and geometric invariant theory. We also classify the SLOCC polynomial invariants and give a degree bound for generators of the invariant ring in the case of $n$-qubit pure states. Of course it is well known that polynomial invariants are not a complete set of invariants for SLOCC.

math.RT↗

arXiv2013

Computing the Tutte Polynomial of Lattice Path Matroids Using Determinantal Circuits

We give a quantum-inspired $O(n^4)$ algorithm computing the Tutte polynomial of a lattice path matroid, where $n$ is the size of the ground set of the matroid. Furthermore, this can be improved to $O(n^2)$ arithmetic operations if we evaluate the Tutte polynomial on a given input, fixing the values of the variables. The best existing algorithm, found in 2004, was $O(n^5)$, and the problem has only been known to be polynomial time since 2003. Conceptually, our algorithm embeds the computation in a determinant using a recently demonstrated equivalence of categories useful for counting problems such as those that appear in simulating quantum systems.

math.CO↗

arXiv2013

The Invariant Ring Of m Matrices Under The Adjoint Action By a Product Of General Linear Groups

Let $V=V_1 \otimes \cdots \otimes V_n$ be a vector space over an algebraically closed field $K$ of characteristic zero with $\dim(V_i)=d_i$. We study the ring of polynomial invariants $K[\operatorname{End}(V)^{\oplus m}]^{\operatorname{GL}_{\mathbf{d}}}$ of $m$ endomorphisms of $V$ under the adjoint action of $\operatorname{GL}_{\mathbf{d}}:=\operatorname{GL}(V_1) \times \cdots \times \operatorname{GL}(V_n)$. We find that the ring is generated by certain generalized trace monomials $\operatorname{Tr}^M_{\sigma}$ where $M$ is a multiset with entries in $[m]=\{1,\dots, m\}$ and $\sigma \in \mathcal{S}_m^n$ is a choice of $n$ permutations of $[m]$. We find that $K[\operatorname{End}(V)^{\oplus m}]^{\operatorname{GL}_{\mathbf{d}}}$ is generated by the $\operatorname{Tr}^M_\sigma$ of degree at most $\frac{3}{8}m\dim(V)^6$.

math.RT↗

arXiv2013

Generalized Counting Constraint Satisfaction Problems With Determinantal Circuits

Generalized counting constraint satisfaction problems include Holant problems with planarity restrictions; polynomial-time algorithms for such problems include matchgates and matchcircuits, which are based on Pfaffians. In particular, they use gates which are expressible in terms of a vector of sub-Pfaffians of a skew-symmetric matrix. We introduce a new type of circuit based instead on determinants, with seemingly different expressive power. In these determinantal circuits, a gate is represented by the vector of all minors of an arbitrary matrix. Determinantal circuits permit a different class of gates. Applications of these circuits include proofs of theorems from algebraic graph theory including the Chung-Langlands formula for the number of rooted spanning forests of a graph and computing Tutte Polynomials of certain matroids. They also give a strategy for simulating quantum circuits with closed timelike curves. Monoidal category theory provides a useful language for discussing such counting problems, turning combinatorial restrictions into categorical properties. We introduce the counting problem in monoidal categories and count-preserving functors as a way to study FP subclasses of problems in settings which are generally #P-hard. Using this machinery we show that, surprisingly, determinantal circuits can be simulated by Pfaffian circuits at quadratic cost.

math.CT↗