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Approximation of Optimal Transport problems with marginal moments constraintsMay 14 2019Optimal Transport (OT) problems arise in a wide range of applications, from physics to economics. Getting numerical approximate solution of these problems is a challenging issue of practical importance. In this work, we investigate the relaxation of the ... More

A dynamical adaptive tensor method for the Vlasov-Poisson systemJun 21 2016A numerical method is proposed to solve the full-Eulerian time-dependent Vlasov-Poisson system in high dimension. The algorithm relies on the construction of a tensor decomposition of the solution whose rank is adapted at each time step. This decomposition ... More

A non-parametric k-nearest neighbour entropy estimatorJun 22 2015A non-parametric k-nearest neighbour based entropy estimator is proposed. It improves on the classical Kozachenko-Leonenko estimator by considering non-uniform probability densities in the region of k-nearest neighbours around each sample point. It aims ... More

Approximated Lax Pairs for the Reduced Order Integration of Nonlinear Evolution EquationsJan 20 2014A reduced-order model algorithm, called ALP, is proposed to solve nonlinear evolution partial differential equations. It is based on approximations of generalized Lax pairs. Contrary to other reduced-order methods, like Proper Orthogonal Decomposition, ... More

An Experimental Approach for Optimising Mobile Agent MigrationsDec 20 2010The field of mobile agent (MA) technology has been intensively researched during the past few years, resulting in the phenomenal proliferation of available MA platforms, all sharing several common design characteristics. Research projects have mainly ... More

Renormalization of gauge theories without cohomologyJan 31 2013Jul 31 2013We investigate the renormalization of gauge theories without assuming cohomological properties. We define a renormalization algorithm that preserves the Batalin-Vilkovisky master equation at each step and automatically extends the classical action till ... More

Weighted power counting, neutrino masses and Lorentz violating extensions of the Standard ModelAug 26 2008Jan 28 2009We study the Standard-Model extensions that have the following features: they violate Lorentz invariance explicitly at high energies; they are unitary, local, polynomial and renormalizable by weighted power counting; they contain the vertex (LH)^2, which ... More

Infinite reduction of couplings in non-renormalizable quantum field theoryMar 16 2005Aug 06 2005I study the problem of renormalizing a non-renormalizable theory with a reduced, eventually finite, set of independent couplings. The idea is to look for special relations that express the coefficients of the irrelevant terms as unique functions of a ... More

Covariant Pauli-Villars Regularization of Quantum Gravity at the One Loop OrderJul 02 1993We study a regularization of the Pauli-Villars kind of the one loop gravitational divergences in any dimension. The Pauli-Villars fields are massive particles coupled to gravity in a covariant and nonminimal way, namely one real tensor and one complex ... More

Global Maximizers for the Sphere Adjoint Fourier Restriction InequalityOct 09 2013Oct 22 2014We show that constant functions are global maximizers for the adjoint Fourier restriction inequality for the sphere.

A finite dimensional filter with exponential conditional densityJan 14 2009In this paper we consider the continuous--time nonlinear filtering problem, which has an infinite--dimensional solution in general, as proved by Chaleyat--Maurel and Michel. There are few examples of nonlinear systems for which the optimal filter is finite ... More

Adler-Bardeen theorem and cancellation of gauge anomalies to all orders in nonrenormalizable theoriesJan 28 2015May 25 2015We prove the Adler-Bardeen theorem in a large class of general gauge theories, including nonrenormalizable ones. We assume that the gauge symmetries are general covariance, local Lorentz symmetry and Abelian and non-Abelian Yang-Mills symmetries, and ... More

Background field method, Batalin-Vilkovisky formalism and parametric completeness of renormalizationNov 12 2013Feb 05 2014We investigate the background field method with the Batalin-Vilkovisky formalism, to generalize known results, study parametric completeness and achieve a better understanding of several properties. In particular, we study renormalization and gauge dependence ... More

Weighted scale invariant quantum field theoriesJan 08 2008Feb 17 2008We study a class of Lorentz violating quantum field theories that contain higher space derivatives, but no higher time derivatives, and become renormalizable in the large N expansion. The fixed points of their renormalization-group flows provide examples ... More

Ward identities and gauge independence in general chiral gauge theoriesJan 27 2015Jul 21 2015Using the Batalin-Vilkovisky formalism, we study the Ward identities and the equations of gauge dependence in potentially anomalous general gauge theories, renormalizable or not. A crucial new term, absent in manifestly nonanomalous theories, is responsible ... More

Renormalization of a class of non-renormalizable theoriesFeb 28 2005Aug 06 2005Certain power-counting non-renormalizable theories, including the most general self-interacting scalar fields in four and three dimensions and fermions in two dimensions, have a simplified renormalization structure. For example, in four-dimensional scalar ... More

Finiteness of quantum gravity coupled with matter in three spacetime dimensionsSep 28 2003Apr 07 2004As it stands, quantum gravity coupled with matter in three spacetime dimensions is not finite. In this paper I show that an algorithmic procedure that makes it finite exists, under certain conditions. To achieve this result, gravity is coupled with an ... More

Absence of higher derivatives in the renormalization of propagators in quantum field theories with infinitely many couplingsDec 02 2002Apr 28 2003I study some aspects of the renormalization of quantum field theories with infinitely many couplings in arbitrary space-time dimensions. I prove that when the space-time manifold admits a metric of constant curvature the propagator is not affected by ... More

An Original Mechanism for the Acceleration of Ultra-High-Energy Cosmic RaysApr 28 2017We suggest that ultra-high-energy (UHE) cosmic rays (CRs) may be accelerated in ultra-relativistic flows via a one-shot mechanism, the "espresso" acceleration, in which already-energetic particles are generally boosted by a factor of $\sim\Gamma^2$ in ... More

Maximizers for the Strichartz inequalityApr 01 2004Aug 19 2006We compute explicitely the best constants and, by solving some functional equations, we find all maximizers for homogeneous Strichartz estimates for the Schrodinger equation and for the wave equation in the cases when the Lebesgue exponent is an even ... More

Tautological Classes of the Stack of Rational Nodal CurvesJan 09 2009This is the second in a series of three papers in which we investigate the rational Chow ring of the stack consisting of nodal curves of genus. Here we define the basic classes: the classes of strata and the Mumford classes.

The general mixture-diffusion SDE and its relationship with an uncertain-volatility option model with volatility-asset decorrelationDec 21 2008In the present paper, given an evolving mixture of probability densities, we define a candidate diffusion process whose marginal law follows the same evolution. We derive as a particular case a stochastic differential equation (SDE) admitting a unique ... More

Some reference formulas for the generating functions of canonical transformationsNov 03 2015Apr 05 2016We study some properties of the canonical transformations in classical mechanics and quantum field theory and give a number of practical formulas concerning their generating functions. First, we give a diagrammatic formula for the perturbative expansion ... More

Deformed dimensional regularization for odd (and even) dimensional theoriesApr 06 2004Aug 07 2004I formulate a deformation of the dimensional-regularization technique that is useful for theories where the common dimensional regularization does not apply. The Dirac algebra is not dimensionally continued, to avoid inconsistencies with the trace of ... More

Nodes as Composite Operators in Matrix ModelsNov 28 1994Nov 29 1994Riemann surfaces with nodes can be described by introducing simple composite operators in matrix models. In the case of the Kontsevich model, it is sufficient to add the quadratic, but ``non-propagating'', term (tr[X])^2 to the Lagrangian. The corresponding ... More

Master Functional And Proper Formalism For Quantum Gauge Field TheoryMay 17 2012Apr 01 2013We develop a general field-covariant approach to quantum gauge theories. Extending the usual set of integrated fields and external sources to "proper" fields and sources, which include partners of the composite fields, we define the master functional ... More

Renormalization and causality violations in classical gravity coupled with quantum matterMay 20 2006Jan 15 2007I prove that classical gravity coupled with quantized matter can be renormalized with a finite number of independent couplings, plus field redefinitions, without introducing higher-derivative kinetic terms in the gravitational sector, but adding vertices ... More

Probability-free models in option pricing: statistically indistinguishable dynamics and historical vs implied volatilityApr 03 2019We investigate whether it is possible to formulate option pricing and hedging models without using probability. We present a model that is consistent with two notions of volatility: a historical volatility consistent with statistical analysis, and an ... More

On the Chow ring of the stack of rational nodal curvesMay 07 2007The goal of this paper is to compute the rational Chow ring of the stack consisting of nodal curves of genus 0 with at most 3 nodes: it is a Q-algebra with 10 generators and 11 relations.

Constant Maturity Credit Default Swap Pricing with Market ModelsDec 22 2008In this work we derive an approximated no-arbitrage market valuation formula for Constant Maturity Credit Default Swaps (CMCDS). We move from the CDS options market model in Brigo (2004), and derive a formula for CMCDS that is the analogous of the formula ... More

Background field method and the cohomology of renormalizationNov 04 2015Apr 05 2016Using the background field method and the Batalin-Vilkovisky formalism, we prove a key theorem on the cohomology of perturbatively local functionals of arbitrary ghost numbers, in renormalizable and nonrenormalizable quantum field theories whose gauge ... More

Adler-Bardeen theorem and manifest anomaly cancellation to all orders in gauge theoriesFeb 26 2014Oct 01 2014We reconsider the Adler-Bardeen theorem for the cancellation of gauge anomalies to all orders, when they vanish at one loop. Using the Batalin-Vilkovisky formalism and combining the dimensional-regularization technique with the higher-derivative gauge ... More

A General Field-Covariant Formulation Of Quantum Field TheoryMay 15 2012Mar 12 2013In all nontrivial cases renormalization, as it is usually formulated, is not a change of integration variables in the functional integral, plus parameter redefinitions, but a set of replacements, of actions and/or field variables and parameters. Because ... More

Weighted power counting and Lorentz violating gauge theories. I: General propertiesAug 26 2008Jan 28 2009We construct local, unitary gauge theories that violate Lorentz symmetry explicitly at high energies and are renormalizable by weighted power counting. They contain higher space derivatives, which improve the behavior of propagators at large momenta, ... More

A note on the dimensional regularization of the Standard Model coupled with Quantum GravityApr 04 2004Jul 06 2004In flat space, gamma5 and the epsilon tensor break the dimensionally continued Lorentz symmetry, but propagators have fully Lorentz invariant denominators. When the Standard Model is coupled with quantum gravity gamma5 breaks the continued local Lorentz ... More

Consistent irrelevant deformations of interacting conformal field theoriesSep 27 2003Nov 04 2003I show that under certain conditions it is possible to define consistent irrelevant deformations of interacting conformal field theories. The deformations are finite or have a unique running scale ("quasi-finite"). They are made of an infinite number ... More

Renormalization of quantum gravity coupled with matter in three dimensionsSep 27 2003Apr 04 2004In three spacetime dimensions, where no graviton propagates, pure gravity is known to be finite. It is natural to inquire whether finiteness survives the coupling with matter. Standard arguments ensure that there exists a subtraction scheme where no Lorentz-Chern-Simons ... More

More on the Subtraction AlgorithmJul 05 1994We go on in the program of investigating the removal of divergences of a generical quantum gauge field theory, in the context of the Batalin-Vilkovisky formalism. We extend to open gauge-algebrae a recently formulated algorithm, based on redefinitions ... More

Aspects of perturbative unitarityJun 20 2016Jul 19 2016We reconsider perturbative unitarity in quantum field theory and upgrade several arguments and results. The minimum assumptions that lead to the largest time equation, the cutting equations and the unitarity equation are identified. Using this knowledge ... More

Weighted power counting and chiral dimensional regularizationMay 13 2014Jun 27 2014We define a modified dimensional-regularization technique that overcomes several difficulties of the ordinary technique, and is specially designed to work efficiently in chiral and parity violating quantum field theories, in arbitrary dimensions greater ... More

Quantum Topological Invariants, Gravitational Instantons and the Topological EmbeddingJul 27 1996Certain topological invariants of the moduli space of gravitational instantons are defined and studied. Several amplitudes of two and four dimensional topological gravity are computed. A notion of puncture in four dimensions, that is particularly meaningful ... More

Counterparty Risk FAQ: Credit VaR, PFE, CVA, DVA, Closeout, Netting, Collateral, Re-hypothecation, WWR, Basel, Funding, CCDS and Margin LendingNov 05 2011Jun 17 2012We present a dialogue on Counterparty Credit Risk touching on Credit Value at Risk (Credit VaR), Potential Future Exposure (PFE), Expected Exposure (EE), Expected Positive Exposure (EPE), Credit Valuation Adjustment (CVA), Debit Valuation Adjustment (DVA), ... More

Supernova remnants as cosmic ray factoriesMar 24 2011In this work we investigate particle acceleration in supernova remnant shocks within a semi-analytical formalism which self-consistently accounts for particle acceleration, amplification of the magnetic field via streaming instability and back-reaction ... More

Metric-Affine Gravity and Cosmology/Aspects of Torsion and non-Metricity in Gravity TheoriesFeb 25 2019This Thesis is devoted to the study of Metric-Affine Theories of Gravity and Applications to Cosmology. The thesis is organized as follows. In the first Chapter we define the various geometrical quantities that characterize a non-Riemannian geometry. ... More

State estimation with nonlinear reduced models. Application to the reconstruction of blood flows with Doppler ultrasound imagesApr 30 2019Over the past years, several fast reconstruction algorithms based on reduced models have been proposed to address the state estimation problem of approximating an unknown function u of a Hilbert space V from measurement observations. Most strategies are ... More

Numerical quadrature in the Brillouin zone for periodic Schrodinger operatorsMay 18 2018As a consequence of Bloch's theorem, the numerical computation of the fermionic ground state density matrices and energies of periodic Schrodinger operators involves integrals over the Brillouin zone. These integrals are difficult to compute numerically ... More

CCP Cleared or Bilateral CSA Trades with Initial/Variation Margins under credit, funding and wrong-way risks: A Unified Valuation ApproachJan 16 2014The introduction of CCPs in most derivative transactions will dramatically change the landscape of derivatives pricing, hedging and risk management, and, according to the TABB group, will lead to an overall liquidity impact about 2 USD trillions. In this ... More

Credit Default Swap Calibration and Counterparty Risk Valuation with a Scenario based First Passage ModelDec 15 2009In this work we develop a tractable structural model with analytical default probabilities depending on a random default barrier and possibly random volatility ideally associated with a scenario based underlying firm debt. We show how to calibrate this ... More

Renormalizable acausal theories of classical gravity coupled with interacting quantum fieldsNov 11 2006Apr 02 2007We prove the renormalizability of various theories of classical gravity coupled with interacting quantum fields. The models contain vertices with dimensionality greater than four, a finite number of matter operators and a finite or reduced number of independent ... More

Vacuum Cherenkov Radiation In Quantum Electrodynamics With High-Energy Lorentz ViolationJan 11 2011Mar 12 2011We study phenomena predicted by a renormalizable, CPT invariant extension of the Standard Model that contains higher-dimensional operators and violates Lorentz symmetry explicitly at energies greater than some scale Lambda_{L}. In particular, we consider ... More

Statistical arbitrage of coherent risk measuresFeb 26 2019We show that coherent risk measures are ineffective in curbing the behaviour of investors with limited liability if the market admits statistical arbitrage opportunities which we term $\rho$-arbitrage for a risk measure $\rho$. We show how to determine ... More

Interest-Rate Modelling in Collateralized Markets: Multiple curves, credit-liquidity effects, CCPsApr 04 2013The market practice of extrapolating different term structures from different instruments lacks a rigorous justification in terms of cash flows structure and market observables. In this paper, we integrate our previous consistent theory for pricing under ... More

Interpolation and smoothingAug 29 2002Sep 10 2002Smoothing is omnipresent in astronomy, because almost always measurements performed at discrete positions in the sky need to be interpolated into a smooth map for subsequent analysis. Still, the statistical properties of different interpolation techniques ... More

Distinguishing extension numbers for $\mathbf R^n$ and $S^n$Aug 25 2014In the setting of a group $\Gamma$ acting faithfully on a set $X$, a $k$-coloring $c: X\rightarrow \{1, 2, ..., k\}$ is called $\Gamma$-distinguishing if the only element of $\Gamma$ that fixes $c$ is the identity element. The distinguishing number $D_\Gamma(X)$ ... More

Philosophy and RelativityMay 30 2007With his General Theory of Relativity, Albert Einstein produced a revolution in our conception of reality and of the knowledge we can obtain from it. This revolution can be viewed from philosophy as leading to one of the great paradigms in the history ... More

NICEST, a near-infrared color excess method tailored for small-scale structuresSep 19 2008Observational data and theoretical calculations show that significant small-scale substructures are present in dark molecular clouds. These inhomogeneities can provide precious hints on the physical conditions inside the clouds, but can also severely ... More

Spectral spaces versus distributive lattices: a dictionaryDec 15 2018The category of distributive lattices is, in classical mathematics, antiequivalent to the category of spectral spaces. We give here some examples and a short dictionary for this antiequivalence. We propose a translation of several abstract theorems (in ... More

Maximum likelihood eigenfunctions of the Fokker Planck equation and Hellinger projectionMar 14 2016We apply the $L^2$ based Fisher-Rao vector-field projection by Brigo, Hanzon and LeGland (1999) to finite dimensional approximations of the Fokker Planck equation on exponential families. We show that if the sufficient statistics are chosen among the ... More

Renormalization of Lorentz violating theoriesJul 17 2007Nov 26 2007We classify the unitary, renormalizable, Lorentz violating quantum field theories of interacting scalars and fermions, obtained improving the behavior of Feynman diagrams by means of higher space derivatives. Higher time derivatives are not generated ... More

18th Workshop on Logic-based methods in Programming Environments (WLPE 2008)Mar 09 2009Mar 26 2009This volume contains the papers presented at WLPE 2008: the 18th Workshop on Logic-based Methods in Programming Environments held on 12th December, 2008 in Udine, Italy. It was held as a satellite workshop of ICLP 2008, the 24th International Conference ... More

Moduli stacks of curves with a fixed dual graphJul 13 2010Sep 07 2010We consider the stack of stable curves of genus g with a given dual graph and we give an explicit desingularization of its closure in the moduli stack of stable curves. We study in particular the one-dimensional substack of curves with at least 3g-4 nodes. ... More

The Chow ring of the stack of cyclic covers of the projective lineMar 22 2010Oct 04 2010In this paper we compute the integral Chow ring of the stack of smooth uniform cyclic covers of the projective line and we give explicit generators.

Bistable Auxetic Mechanical Metamaterials Inspired by Ancient Geometric MotifsDec 18 2016Auxetic materials become thicker rather than thinner when stretched, exhibiting an unusual negative Poisson's ratio well suited for designing shape transforming metamaterials. Current auxetic designs, however, are often monostable and cannot maintain ... More

The Chow Ring of the Stack of Smooth Plane CubicsJun 20 2016Jan 14 2018We give an explicit presentation of the integral Chow ring of a stack of smooth plane cubics. We also determine some relations in the general case of hypersurfaces of any dimension and degree.

The integral Chow ring of the stack of at most 1-nodal rational curvesMay 09 2006Mar 27 2007We give a presentation for the stack of rational curves with at most 1 node as the quotient by GL(3) of an open set in a 6-dimensional irreducible representation. We then use equivariant intersection theory to calculate the integral Chow ring of this ... More

Liquidity-adjusted Market Risk Measures with Stochastic Holding PeriodSep 20 2010Oct 20 2010Within the context of risk integration, we introduce in risk measurement stochastic holding period (SHP) models. This is done in order to obtain a `liquidity-adjusted risk measure' characterized by the absence of a fixed time horizon. The underlying assumption ... More

The integral Chow ring of the stack of hyperelliptic curves of even genusDec 28 2007Let $g$ be an even positive integer. In this paper we compute the integral Chow ring of the stack of smooth hyperelliptic curves of genus $g$.

Credit Default Swap Calibration and Equity Swap Valuation under Counterparty Risk with a Tractable Structural ModelDec 15 2009In this paper we develop a tractable structural model with analytical default probabilities depending on some dynamics parameters, and we show how to calibrate the model using a chosen number of Credit Default Swap (CDS) market quotes. We essentially ... More

Twisted N=2 Supergravity as Topological Gravity in Four DimensionsAug 11 1992We show that the BRST quantum version of pure D=4 N=2 supergravity can be topologically twisted, to yield a formulation of topological gravity in four dimensions. The topological BRST complex is just a rearrangement of the old BRST complex, that partly ... More

Tate's Algorithm for F-theory GUTs with two U(1)sDec 12 2014We present a systematic study of elliptic fibrations for F-theory realizations of gauge theories with two U(1) factors. In particular, we determine a new class of SU(5) x U(1)^2 fibrations, which can be used to engineer Grand Unified Theories, with multiple, ... More

Projection based dimensionality reduction for measure valued evolution equations in statistical manifoldsJan 16 2016Oct 26 2016We propose a dimensionality reduction method for infinite-dimensional measure-valued evolution equations such as the Fokker-Planck partial differential equation or the Kushner-Stratonovich resp. Duncan-Mortensen-Zakai stochastic partial differential equations ... More

Nef and semiample divisors on rational surfacesApr 21 2011Mar 25 2013In this paper we study smooth projective rational surfaces, defined over an algebraically closed field of any characteristic, with pseudo-effective anticanonical divisor. We provide a necessary and sufficient condition in order for any nef divisor to ... More

Cores of simplicial complexesMar 12 2007We introduce a method to reduce the study of the topology of a simplicial complex to that of a simpler one. We give some applications of this method to complexes arising from graphs. As a consequence, we answer some questions raised in [R.Ehrenborg, G.Hetyei, ... More

Optimal approximation of SDEs on submanifolds: the Ito-vector and Ito-jet projectionsOct 12 2016Jul 07 2017We define two new notions of projection of a stochastic differential equation (SDE) onto a submanifold: the Ito-vector and Ito-jet projections. This allows one to systematically develop low dimensional approximations to high dimensional SDEs using differential ... More

Inflation securities valuation with macroeconomic-based no-arbitrage dynamicsMar 30 2014Jul 26 2014We develop a model to price inflation and interest rates derivatives using continuous-time dynamics that have some links with macroeconomic monetary DSGE models equipped with a Taylor rule: in particular, the reaction function of the central bank, the ... More

CCPs, Central Clearing, CSA, Credit Collateral and Funding Costs Valuation FAQ: Re-hypothecation, CVA, Closeout, Netting, WWR, Gap-Risk, Initial and Variation Margins, Multiple Discount Curves, FVA?Nov 30 2013Dec 03 2013We present a dialogue on Funding Costs and Counterparty Credit Risk modeling, inclusive of collateral, wrong way risk, gap risk and possible Central Clearing implementation through CCPs. This framework is important following the fact that derivatives ... More

IEAD: A Novel One-Line Interface to Query Astronomical Science ArchivesFeb 27 2012In this article I present IEAD, a new interface for astronomical science databases. It is based on a powerful, yet simple, syntax designed to completely abstract the user from the structure of the underlying database. The programming language chosen for ... More

On three filtering problems arising in mathematical financeDec 21 2008Three situations in which filtering theory is used in mathematical finance are illustrated at different levels of detail. The three problems originate from the following different works: 1) On estimating the stochastic volatility model from observed bilateral ... More

Gauged Hyperinstantons and Monopole EquationsNov 28 1994Dec 19 1994The monopole equations in the dual abelian theory of the N=2 gauge-theory, recently proposed by Witten as a new tool to study topological invariants, are shown to be the simplest elements in a class of instanton equations that follow from the improved ... More

Topological Sigma-Models in Four Dimensions and Triholomorphic MapsJun 17 1993Jun 19 1993It is well-known that topological sigma-models in 2 dimensions constitute a path-integral approach to the study of holomorphic maps from a Riemann surface S to an almost complex manifold K, the most interesting case being that where K is a Kahler manifold. ... More

Dimensionally continued infinite reduction of couplingsSep 27 2005Jan 18 2006The infinite reduction of couplings is a tool to consistently renormalize a wide class of non-renormalizable theories with a reduced, eventually finite, set of independent couplings, and classify the non-renormalizable interactions. Several properties ... More

The Chow Ring of the Stack of Smooth Plane CubicsJun 20 2016We give an explicit presentation of the integral Chow ring of a stack of smooth plane cubics. We also determine some relations in the general case of hypersurfaces of any dimension and degree.

Scale transformations in metric-affine geometryOct 29 2018This article presents an exhaustive classification of metric-affine theories according to their scale symmetries. First it is clarified that there are three relevant definitions of a scale transformation. These correspond to a projective transformation ... More

Modeling dark energy through an Ising fluid with network interactionsApr 13 2013We show that the dark energy effects can be modeled by using an \emph{Ising perfect fluid} with network interactions, whose low redshift equation of state, i.e. $\omega_0$, becomes $\omega_0=-1$ as in the $\Lambda$CDM model. In our picture, dark energy ... More

Effect of Cosmic Rays on the Evolution and Momentum Deposition of Supernova RemnantsApr 25 2018Sep 05 2018Using a semianalytical approach based on the thin-shell approximation, we calculate the long-term evolution of supernova remnants (SNRs) while also accounting for the cosmic rays (CRs) accelerated at their blast waves. Our solution reproduces the results ... More

Renormalization Of High-Energy Lorentz Violating QEDDec 01 2009May 09 2010We study a QED extension that is unitary, CPT invariant and super-renormalizable, but violates Lorentz symmetry at high energies, and contains higher-dimension operators (LVQED). Divergent diagrams are only one- and two-loop. We compute the one-loop renormalizations ... More

On a question of DolgachevJun 06 2018Jul 07 2018For each even, positive integer $n$, we define a rational self-map on the space of plane curves of degree $n$, using classical contravariants. In the case of plane quartics, we show that the degree of this map is 15. This answers a question of Dolgachev ... More

Reconstructing general plane quartics from their inflection linesNov 15 2017Apr 20 2018Let $C$ be a general plane quartic and let ${\rm Fl}(C)$ denote the configuration of inflection lines of $C$. We show that if $D$ is any plane quartic with the same configuration of inflection lines ${\rm Fl}(C)$, then the quartics $C$ and $D$ coincide. ... More

Static vs adapted optimal execution strategies in two benchmark trading modelsSep 18 2016We consider the optimal solutions to the trade execution problem in the two different classes of i) fully adapted or adaptive and ii) deterministic or static strategies, comparing them. We do this in two different benchmark models. The first model is ... More

Algebra in Bishop's style: some major features of the book "A Course in Constructive Algebra'' by Mines, Richman, and RuitenburgMar 11 2019The book "A Course in Constructive Algebra" (1988) shows the way of understanding classical basic algebra in a constructive style similar to Bishop's Constructive Mathematics. Classical theorems are revisited, with a new flavour, and become much more ... More

Spectral spaces versus distributive lattices: a dictionaryDec 15 2018Apr 06 2019English abstract The category of distributive lattices is, in classical mathematics, antiequivalent to the category of spectral spaces. We give here some examples and a short dictionary for this antiequivalence. We propose a translation of several abstract ... More

Abstract Program Slicing: an Abstract Interpretation-based approach to Program SlicingMay 17 2016In the present paper we formally define the notion of abstract program slicing, a general form of program slicing where properties of data are considered instead of their exact value. This approach is applied to a language with numeric and reference values, ... More

Projection based dimensionality reduction for measure valued evolution equations in statistical manifoldsJan 16 2016Mar 02 2016We propose a dimensionality reduction method for infinite-dimensional measure-valued evolution equations such as the Fokker-Planck partial differential equation or the Kushner-Stratonovich resp. Duncan-Mortensen-Zakai stochastic partial differential equations ... More

Arbitrage-free Pricing of Credit Index Options: The no-armageddon pricing measure and the role of correlation after the subprime crisisDec 22 2008In this work we consider three problems of the standard market approach to pricing of credit index options: the definition of the index spread is not valid in general, the usually considered payoff leads to a pricing which is not always defined, and the ... More

Disentangling wrong-way risk: pricing CVA via change of measures and drift adjustmentNov 09 2016A key driver of Credit Value Adjustment (CVA) is the possible dependency between exposure and counterparty credit risk, known as Wrong-Way Risk (WWR). At this time, addressing WWR in a both sound and tractable way remains challenging: arbitrage-free setups ... More

Renormalization Of High-Energy Lorentz Violating Four Fermion ModelsFeb 13 2010May 09 2010We study the one-loop renormalization of high-energy Lorentz violating four fermion models. We derive general formulas and then consider a number of specific models. We study the conditions for asymptotic freedom and give a practical method to determine ... More

On the Spectrum of Electrons Accelerated in Supernova RemnantsMay 17 2019Using a semi-analytic model of non-linear diffusive shock acceleration, we model the spectrum of cosmic ray (CR) electrons accelerated by supernova remnants (SNRs). Because electrons experience synchrotron losses in the amplified magnetic fields characteristic ... More

On minimal rational elliptic surfacesFeb 01 2015May 10 2015We construct $13$ projective $\mathbb{Q}$-factorial Fano toric varieties and show that for any minimal rational elliptic surface $X$ there is one such toric variety $Z_X$ and a divisor class $\delta_X\in {\rm Cl}(Z_X)$ such that the number of $(-1)$-curves ... More

The surface parametrizing cuboidsSep 02 2010We study the surface \bar{S} parametrizing cuboids: it is defined by the equations relating the sides, face diagonals and long diagonal of a rectangular box. It is an open problem whether a `rational box' exists, i.e., a rectangular box all of whose sides, ... More

Recovering plane curves of low degree from their inflection lines and inflection pointsOct 13 2011In this paper we consider the following problem: is it possible to recover a smooth plane curve of degree at least three from its inflection lines? We answer positively to the posed question for a general smooth plane quartic curve, making the additional ... More