David H. Cohen - Swarthmore College

David H. Cohen
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David H. Cohen
Swarthmore College
United States

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Solar and Stellar Astrophysics (20)
High Energy Astrophysical Phenomena (7)
Mathematics - Numerical Analysis (7)
Computer Science - Computational Complexity (6)
Mathematics - Group Theory (6)
Earth and Planetary Astrophysics (4)
Computer Science - Artificial Intelligence (4)
Computer Science - Discrete Mathematics (4)
Mathematics - Information Theory (2)
Computer Science - Data Structures and Algorithms (2)
Computer Science - Information Theory (2)
Physics - Medical Physics (1)
Computer Science - Logic in Computer Science (1)
Quantitative Biology - Molecular Networks (1)
Mathematics - Algebraic Topology (1)
Mathematics - K-Theory and Homology (1)
Instrumentation and Methods for Astrophysics (1)
Mathematics - Operator Algebras (1)
Statistics - Applications (1)
Computer Science - Computer Vision and Pattern Recognition (1)
Mathematics - Dynamical Systems (1)
Mathematics - Functional Analysis (1)
Statistics - Machine Learning (1)

Publications Authored By David H. Cohen

We give a new obstruction to translation-like actions on nilpotent groups. Suppose we are given two finitely generated torsion free nilpotent groups with the same degree of polynomial growth, but non-isomorphic Carnot completions (asymptotic cones). We show that there exists no injective Lipschitz function from one group to the other. Read More

Singleton arc consistency is an important type of local consistency which has been recently shown to solve all constraint satisfaction problems (CSPs) over constraint languages of bounded width. We aim to characterise all classes of CSPs defined by a forbidden pattern that are solved by singleton arc consistency and closed under removing constraints. We identify five new patterns whose absence ensures solvability by singleton arc consistency, four of which are provably maximal and three of which generalise 2-SAT. Read More

For finitely generated groups H and G, equipped with word metrics, a translation-like action of H on G is a free action such that each element of H acts by a map which has finite distance from the identity map in the uniform metric. For example, if H is a subgroup of G, then right translation by elements of H yields a translation-like action of H on G. Whyte asked whether a group with no translation-like action by a Baumslag-Solitar group must be hyperbolic, where the free abelian group of rank 2 is understood to be a Baumslag-Solitar group. Read More

A space X is said to be Lipschitz 1-connected if every L-Lipschitz loop in X bounds a O(L)-Lipschitz disk. A Lipschitz 1-connected space admits a quadratic isoperimetric inequality, but it is unknown whether the converse is true. Cornulier and Tessera showed that certain solvable Lie groups have quadratic isoperimetric inequalities, and we extend their result to show that these groups are Lipschitz 1-connected. Read More

Phase synchronisation in multichannel EEG is known as the manifestation of functional brain connectivity. Traditional phase synchronisation studies are mostly based on time average synchrony measures hence do not preserve the temporal evolution of the phase difference. Here we propose a new method to show the existence of a small set of unique phase synchronised patterns or "states" in multi-channel EEG recordings, each "state" being stable of the order of ms, from typical and pathological subjects during face perception tasks. Read More

We conducted a survey of seven magnetic O and eleven B-type stars with masses above $8M_{\odot}$ using the Very Large Array in the 1cm, 3cm and 13cm bands. The survey resulted in a detection of two O and two B-type stars. While the detected O-type stars - HD 37742 and HD 47129 - are in binary systems, the detected B-type stars, HD 156424 and ALS 9522, are not known to be in binaries. Read More

Multiple input multiple output (MIMO) radar exhibits several advantages with respect to traditional radar array systems in terms of flexibility and performance. However, MIMO radar poses new challenges for both hardware design and digital processing. In particular, achieving high azimuth resolution requires a large number of transmit and receive antennas. Read More

The binary Constraint Satisfaction Problem (CSP) is to decide whether there exists an assignment to a set of variables which satisfies specified constraints between pairs of variables. A binary CSP instance can be presented as a labelled graph encoding both the forms of the constraints and where they are imposed. We consider subproblems defined by restricting the allowed form of this graph. Read More

We present novel geometric numerical integrators for Hunter--Saxton-like equations by means of new multi-symplectic formulations and known Hamiltonian structures of the problems. We consider the Hunter--Saxton equation, the modified Hunter--Saxton equation, and the two-component Hunter--Saxton equation. Multi-symplectic discretisations based on these new formulations of the problems are exemplified by means of the explicit Euler box scheme, and Hamiltonian-preserving discretisations are exemplified by means of the discrete variational derivative method. Read More

We present the design and hardware implementation of a radar prototype that demonstrates the principle of a sub-Nyquist collocated multiple-input multiple-output (MIMO) radar. The setup allows sampling in both spatial and spectral domains at rates much lower than dictated by the Nyquist sampling theorem. Our prototype realizes an X-band MIMO radar that can be configured to have a maximum of 8 transmit and 10 receive antenna elements. Read More

We study methods for transforming valued constraint satisfaction problems (VCSPs) to binary VCSPs. First, we show that the standard dual encoding preserves many aspects of the algebraic properties that capture the computational complexity of VCSPs. Second, we extend the reduction of CSPs to binary CSPs described by Bulin et al. Read More

Slowly rotating magnetic massive stars develop "dynamical magnetospheres" (DM's), characterized by trapping of stellar wind outflow in closed magnetic loops, shock heating from collision of the upflow from opposite loop footpoints, and subsequent gravitational infall of radiatively cooled material. In 2D and 3D magnetohydrodynamic (MHD) simulations the interplay among these three components is spatially complex and temporally variable, making it difficult to derive observational signatures and discern their overall scaling trends.Within a simplified, steady-state analysis based on overall conservation principles, we present here an "analytic dynamical magnetosphere" (ADM) model that provides explicit formulae for density, temperature and flow speed in each of these three components -- wind outflow, hot post-shock gas, and cooled inflow -- as a function of colatitude and radius within the closed (presumed dipole) field lines of the magnetosphere. Read More

We study an explicit exponential scheme for the time discretisation of stochastic Schr\"odinger equations driven by additive or multiplicative Ito noise. The numerical scheme is shown to converge with strong order $1$ if the noise is additive and with strong order $1/2$ for multiplicative noise. In addition, if the noise is additive, we show that the exact solutions of our problems satisfy trace formulas for the expected mass, energy, and momentum (i. Read More

We present a multi-wavelength (X-ray to optical) analysis, based on non-local thermodynamic equilibrium photospheric+wind models, of the B0 Ia-supergiant: $\epsilon$~Ori. The aim is to test the consistency of physical parameters, such as the mass-loss rate and CNO abundances, derived from different spectral bands. The derived mass-loss rate is $\dot{M}/\sqrt{f_\infty}\sim$1. Read More

We give strongly aperiodic subshifts of finite type on every hyperbolic surface group; more generally, for each pair of expansive primitive symbolic substitution systems with incommensurate growth rates, we construct strongly aperiodic subshifts of finite type on their orbit graphs. Read More

In this paper we report 23 magnetic field measurements of the B3IV star HD 23478: 12 obtained from high resolution Stokes $V$ spectra using the ESPaDOnS (CFHT) and Narval (TBL) spectropolarimeters, and 11 from medium resolution Stokes $V$ spectra obtained with the DimaPol spectropolarimeter (DAO). HD 23478 was one of two rapidly rotating stars identified as potential "centrifugal magnetosphere" hosts based on IR observations from the Apache Point Observatory Galactic Evolution Experiment survey. We derive basic physical properties of this star including its mass ($M=6. Read More

We explore aspects of dilation theory in the finite dimensional case and show that for a commuting $n$-tuple of operators $T=(T_1,... Read More

A fully discrete approximation of the semi-linear stochastic wave equation driven by multiplicative noise is presented. A standard linear finite element approximation is used in space and a stochastic trigonometric method for the temporal approximation. This explicit time integrator allows for mean-square error bounds independent of the space discretisation and thus do not suffer from a step size restriction as in the often used St\"ormer-Verlet-leap-frog scheme. Read More

Variable or value elimination in a constraint satisfaction problem (CSP) can be used in preprocessing or during search to reduce search space size. A variable elimination rule (value elimination rule) allows the polynomial-time identification of certain variables (domain elements) whose elimination, without the introduction of extra compensatory constraints, does not affect the satisfiability of an instance. We show that there are essentially just four variable elimination rules and three value elimination rules defined by forbidding generic sub-instances, known as irreducible existential patterns, in arc-consistent CSP instances. Read More

A subshift on a group G is a closed, G-invariant subset of A^G, for some finite set A. It is said to be a subshift of finite type (SFT) if it is defined by a finite collection of 'forbidden patterns', to be strongly aperiodic if all point stabilizers are trivial, and weakly aperiodic if all point stabilizers are infinite index in G. We show that groups with at least 2 ends have a strongly aperiodic SFT, and that having such an SFT is a QI invariant for finitely presented torsion free groups. Read More

We present a new multi-symplectic formulation of constrained Hamiltonian partial differential equations, and we study the associated local conservation laws. A multi-symplectic discretisation based on this new formulation is exemplified by means of the Euler box scheme. When applied to the wave map equation, this numerical scheme is explicit, preserves the constraint and can be seen as a generalisation of the Shake algorithm for constrained mechanical systems. Read More

This paper proposes a novel conservative method for numerical computation of general stochastic differential equations in the Stratonovich sense with a conserved quantity. We show that the mean-square order of the method is $1$ if noises are commutative and that the weak order is also $1$. Since the proposed method may need the computation of a deterministic integral, we analyse the effect of the use of quadrature formulas on the convergence orders. Read More

Magnetically confined winds of early-type stars are expected to be sources of bright and hard X-rays. To clarify the systematics of the observed X-ray properties, we have analyzed a large series of Chandra and XMM observations, corresponding to all available exposures of known massive magnetic stars (over 100 exposures covering ~60% of stars compiled in the catalog of Petit et al. 2013). Read More

We present a new method for using measured X-ray emission line fluxes from O stars to determine the shock-heating rate due to instabilities in their radiation-driven winds. The high densities of these winds means that their embedded shocks quickly cool by local radiative emission, while cooling by expansion should be negligible. Ignoring for simplicity any non-radiative mixing or conductive cooling, the method presented here exploits the idea that the cooling post-shock plasma systematically passes through the temperature characteristic of distinct emission lines in the X-ray spectrum. Read More

Gromov conjectured that any irreducible lattice in a symmetric space of rank at least 3 should have at most polynomial Dehn function. We prove that the lattice Sp(2p;Z) has quadratic Dehn function when p is at least 5. By results of Broaddus, Farb, and Putman, this implies that the Torelli group in large genus is at most exponentially distorted. Read More

We use 2D MHD simulations to examine the effects of radiative cooling and inverse Compton (IC) cooling on X-ray emission from magnetically confined wind shocks (MCWS) in magnetic massive stars with radiatively driven stellar winds. For the standard dependence of mass loss rate on luminosity $\Mdot \sim L^{1.7} $, the scaling of IC cooling with $L$ and radiative cooling with $\Mdot$ means that IC cooling become formally more important for lower luminosity stars. Read More

For trigonometric and modified trigonometric integrators applied to oscillatory Hamiltonian differential equations with one or several constant high frequencies, near-conservation of the total and oscillatory energies are shown over time scales that cover arbitrary negative powers of the step size. This requires non-resonance conditions between the step size and the frequencies, but in contrast to previous results the results do not require any non-resonance conditions among the frequencies. The proof uses modulated Fourier expansions with appropriately modified frequencies. Read More

We quantitatively investigate the extent of wind absorption signatures in the X-ray grating spectra of all non-magnetic, effectively single O stars in the Chandra archive via line profile fitting. Under the usual assumption of a spherically symmetric wind with embedded shocks, we confirm previous claims that some objects show little or no wind absorption. However, many other objects do show asymmetric and blue shifted line profiles, indicative of wind absorption. Read More

We study the complexity of constraint satisfaction problems involving global constraints, i.e., special-purpose constraints provided by a solver and represented implicitly by a parametrised algorithm. Read More

The \emph{Workflow Satisfiability Problem (WSP)} is a problem of practical interest that arises whenever tasks need to be performed by authorized users, subject to constraints defined by business rules. We are required to decide whether there exists a \emph{plan} -- an assignment of tasks to authorized users -- such that all constraints are satisfied. Several bespoke algorithms have been constructed for solving the WSP, optimised to deal with constraints (business rules) of particular types. Read More

We fit X-ray emission line profiles in high resolution XMM-Newton and Chandra grating spectra of the early O supergiant Zeta Pup with models that include the effects of porosity in the stellar wind. We explore the effects of porosity due to both spherical and flattened clumps. We find that porosity models with flattened clumps oriented parallel to the photosphere provide poor fits to observed line shapes. Read More

Molecular biology knowledge can be systematically represented in a computer-readable form as a comprehensive map of molecular interactions. There exist a number of maps of molecular interactions containing detailed description of various cell mechanisms. It is difficult to explore these large maps, to comment their content and to maintain them. Read More

X-ray satellites since Einstein have empirically established that the X-ray luminosity from single O-stars scales linearly with bolometric luminosity, Lx ~ 10^{-7} Lbol. But straightforward forms of the most favored model, in which X-rays arise from instability-generated shocks embedded in the stellar wind, predict a steeper scaling, either with mass loss rate Lx ~ Mdot ~ Lbol^{1.7} if the shocks are radiative, or with Lx ~ Mdot^{2} ~ Lbol^{3. Read More

Discrete optimisation problems arise in many different areas and are studied under many different names. In many such problems the quantity to be optimised can be expressed as a sum of functions of a restricted form. Here we present a unifying theory of complexity for problems of this kind. Read More

We prove a homological stability theorem for congruence subgroups of symplectic groups. From this theorem, we deduce a generalization of a theorem of Borel showing that certain homology groups of a congruence subgroup do not depend on the level of the congruence subgroup. Read More

We have compiled a list of 36 O+O and 89 Wolf-Rayet binary candidates in the Milky Way and Magellanic clouds detected with the Chandra, XMM-Newton and ROSAT satellites to probe the connection between their X-ray properties and their system characteristics. Of the WR binaries with published parameters, all but two have kT > 0.9 keV. Read More

We present a generalised formalism for treating the porosity-associated reduction in continuum opacity that occurs when individual clumps in a stochastic medium become optically thick. We consider geometries resulting in either isotropic or anisotropic effective opacity, and, in addition to an idealised model in which all clumps have the same local overdensity and scale, we also treat an ensemble of clumps with optical depths set by Markovian statistics. This formalism is then applied to the specific case of bound-free absorption of X-rays in hot star winds, a process not directly affected by clumping in the optically thin limit. Read More

X-ray satellites since Einstein have empirically established that the X-ray luminosity from single O-stars scales linearly with bolometric luminosity, Lx ~ 10^-7 Lbol. But straightforward forms of the most favored model, in which X-rays arise from instability-generated shocks embedded in the stellar wind, predict a steeper scaling, either with mass loss rate Lx ~ Mdot ~ Lbol^1.7 if the shocks are radiative, or with Lx ~ Lx ~ Mdot^2 ~ Lbol^3. Read More

We propose a fully discretised numerical scheme for the hyperelastic rod wave equation on the line. The convergence of the method is established. Moreover, the scheme can handle the blow-up of the derivative which naturally occurs for this equation. Read More

Affiliations: 1Swarthmore College, 2West Chester University, 3NASA/Goddard Space Flight Center, 4Swarthmore College, 5Swarthmore College, 6University of Delaware, Bartol Research Institute, 7Space Telescope Science Institute, 8University of Delaware, Bartol Research Institute

We present analysis of both the resolved X-ray emission line profiles and the broadband X-ray spectrum of the O2 If* star HD 93129A, measured with the Chandra HETGS. This star is among the earliest and most massive stars in the Galaxy, and provides a test of the embedded wind shock scenario in a very dense and powerful wind. A major new result is that continuum absorption by the dense wind is the primary cause of the hardness of the observed X-ray spectrum, while intrinsically hard emission from colliding wind shocks contributes less than 10% of the X-ray flux. Read More

The constraint satisfaction problem (CSP) is a general problem central to computer science and artificial intelligence. Although the CSP is NP-hard in general, considerable effort has been spent on identifying tractable subclasses. The main two approaches consider structural properties (restrictions on the hypergraph of constraint scopes) and relational properties (restrictions on the language of constraint relations). Read More

The Chandra Carina Complex contains 200 known O- and B type stars. The Chandra survey detected 68 of the 70 O stars and 61 of 127 known B0-B3 stars. We have assembled a publicly available optical/X-ray database to identify OB stars that depart from the canonical Lx/Lbol relation, or whose average X-ray temperatures exceed 1 keV. Read More

The Great Nebula in Carina provides an exceptional view into the violent massive star formation and feedback that typifies giant HII regions and starburst galaxies. We have mapped the Carina star-forming complex in X-rays, using archival Chandra data and a mosaic of 20 new 60ks pointings using the Chandra X-ray Observatory's Advanced CCD Imaging Spectrometer, as a testbed for understanding recent and ongoing star formation and to probe Carina's regions of bright diffuse X-ray emission. This study has yielded a catalog of properties of >14,000 X-ray point sources; >9800 of them have multiwavelength counterparts. Read More

X-rays give direct evidence of instabilities, time-variable structure, and shock heating in the winds of O stars. The observed broad X-ray emission lines provide information about the kinematics of shock-heated wind plasma, enabling us to test wind-shock models. And their shapes provide information about wind absorption, and thus about the wind mass-loss rates. Read More

We present a method for computing the net transmission of X-rays emitted by shock-heated plasma distributed throughout a partially optically thick stellar wind from a massive star. We find the transmission by an exact integration of the formal solution, assuming that the emitting plasma and absorbing plasma are mixed at a constant mass ratio above some minimum radius, below which there is assumed to be no emission. This model is more realistic than either the slab absorption associated with a corona at the base of the wind or the exospheric approximation that assumes that all observed X-rays are emitted without attenuation from above the radius of optical depth unity. Read More

Affiliations: 1Swarthmore College, 2NASA-GSFC, 3Swarthmore College, 4Univ. Pittsburgh, 5Univ. Pittsburgh, 6Univ. Delaware, 7Univ. Delaware

We fit every emission line in the high-resolution Chandra grating spectrum of zeta Pup with an empirical line profile model that accounts for the effects of Doppler broadening and attenuation by the bulk wind. For each of sixteen lines or line complexes that can be reliably measured, we determine a best-fitting fiducial optical depth, tau_* = kappa*Mdot/4{pi}R_{\ast}v_{\infty}, and place confidence limits on this parameter. These sixteen lines include seven that have not previously been reported on in the literature. Read More

We present new high-resolution mid-infrared imaging, high-resolution optical spectroscopy, and Chandra grating X-ray spectroscopy of the weak-lined T Tauri star DoAr 21. DoAr 21 (age < 10^6 yr and mass ~ 2.2 M_sun) is a strong X-ray emitter, with conflicting evidence in the literature about its disk properties. Read More