Multiplicative Noise: Applications in Cosmology and Field Theory

Physical situations involving multiplicative noise arise generically in cosmology and field theory. In this paper, the focus is first on exact nonlinear Langevin equations, appropriate in a cosmologica setting, for a system with one degree of freedom. The Langevin equations are derived using an appropriate time-dependent generalization of a model due to Zwanzig. These models are then extended to field theories and the generation of multiplicative noise in such a context is discussed. Important issues in both the cosmological and field theoretic cases are the fluctuation-dissipation relations and the relaxation time scale. Of some importance in cosmology is the fact that multiplicative noise can substantially reduce the relaxation time. In the field theoretic context such a noise can lead to a significant enhancement in the nucleation rate of topological defects.Comment: 21 pages, LaTex, LA-UR-93-210

Deficits in explicit emotion regulation in bipolar disorder: A systematic review

Background: This study aimed to compile and synthesize studies investigating explicit emotion regulation in patients with bipolar disorder and individuals at risk of developing bipolar disorder. The importance of explicit emotion regulation arises from its potential role as a marker for bipolar disorders in individuals at risk and its potent role in therapy for bipolar disorder patients. Methods: To obtain an exhaustive compilation of studies dealing specifically with explicit emotion regulation in bipolar disorder, we conducted a systematic literature search in four databases. In the 15 studies we included in our review, the emotion-regulation strategies maintenance, distraction, and reappraisal (self-focused and situation-focused) were investigated partly on a purely behavioral level and partly in conjunction with neural measures. The samples used in the identified studies included individuals at increased risk of bipolar disorder, patients with current affective episodes, and patients with euthymic mood state. Results: In summary, the reviewed studies' results indicate impairments in explicit emotion regulation in individuals at risk for bipolar disorder, patients with manic and depressive episodes, and euthymic patients. These deficits manifest in subjective behavioral measures as well as in neural aberrations. Further, our review reveals a discrepancy between behavioral and neural findings regarding explicit emotion regulation in individuals at risk for bipolar disorders and euthymic patients. While these groups often do not differ significantly in behavioral measures from healthy and low-risk individuals, neural differences are mainly found in frontostriatal networks. Conclusion: We conclude that these neural aberrations are a potentially sensitive measure of the probability of occurrence and recurrence of symptoms of bipolar disorders and that strengthening this frontostriatal route is a potentially protective measure for individuals at risk and patients who have bipolar disorders

Higher-Order Termination: from Kruskal to Computability

Termination is a major question in both logic and computer science. In logic, termination is at the heart of proof theory where it is usually called strong normalization (of cut elimination). In computer science, termination has always been an important issue for showing programs correct. In the early days of logic, strong normalization was usually shown by assigning ordinals to expressions in such a way that eliminating a cut would yield an expression with a smaller ordinal. In the early days of verification, computer scientists used similar ideas, interpreting the arguments of a program call by a natural number, such as their size. Showing the size of the arguments to decrease for each recursive call gives a termination proof of the program, which is however rather weak since it can only yield quite small ordinals. In the sixties, Tait invented a new method for showing cut elimination of natural deduction, based on a predicate over the set of terms, such that the membership of an expression to the predicate implied the strong normalization property for that expression. The predicate being defined by induction on types, or even as a fixpoint, this method could yield much larger ordinals. Later generalized by Girard under the name of reducibility or computability candidates, it showed very effective in proving the strong normalization property of typed lambda-calculi..

Algebraic totality, towards completeness

Finiteness spaces constitute a categorical model of Linear Logic (LL) whose objects can be seen as linearly topologised spaces, (a class of topological vector spaces introduced by Lefschetz in 1942) and morphisms as continuous linear maps. First, we recall definitions of finiteness spaces and describe their basic properties deduced from the general theory of linearly topologised spaces. Then we give an interpretation of LL based on linear algebra. Second, thanks to separation properties, we can introduce an algebraic notion of totality candidate in the framework of linearly topologised spaces: a totality candidate is a closed affine subspace which does not contain 0. We show that finiteness spaces with totality candidates constitute a model of classical LL. Finally, we give a barycentric simply typed lambda-calculus, with booleans ${\mathcal{B}}$ and a conditional operator, which can be interpreted in this model. We prove completeness at type ${\mathcal{B}}^n\to{\mathcal{B}}$ for every n by an algebraic method

Strangeness Enhancement in p+Ap+A and S+AS+A Interactions at SPS Energies

The systematics of strangeness enhancement is calculated using the HIJING and VENUS models and compared to recent data on $\,pp\,$, $\,pA\,$ and $\,AA\,$ collisions at CERN/SPS energies ($200A\,\, GeV\,$). The HIJING model is used to perform a {\em linear} extrapolation from $pp$ to $AA$. VENUS is used to estimate the effects of final state cascading and possible non-conventional production mechanisms. This comparison shows that the large enhancement of strangeness observed in $S+Au$ collisions, interpreted previously as possible evidence for quark-gluon plasma formation, has its origins in non-equilibrium dynamics of few nucleon systems. % Strangeness enhancement %is therefore traced back to the change in the production dynamics %from $pp$ to minimum bias $pS$ and central $SS$ collisions. A factor of two enhancement of $\Lambda^{0}$ at mid-rapidity is indicated by recent $pS$ data, where on the average {\em one} projectile nucleon interacts with only {\em two} target nucleons. There appears to be another factor of two enhancement in the light ion reaction $SS$ relative to $pS$, when on the average only two projectile nucleons interact with two target ones.Comment: 29 pages, 8 figures in uuencoded postscript fil

New mechanism for the production of the extremely fast light particles in heavy-ion collisions in the Fermi energy domain

Employing a four-body classical model, various mechanisms responsible for the production of fast light particles in heavy ion collisions at low and intermediate energies have been studied. It has been shown that at energies lower than 50 A MeV, light particles of velocities of more than two times higher than the projectile velocities are produced due to the acceleration of the target light-particles by the mean field of the incident nucleus. It has also been shown that precision experimental reaction research in normal and inverse kinematics is likely to provide vital information about which mechanism is dominant in the production of fast light particles.Comment: 4 pages, 3 figures, LaTeX, to be published in Proceedings of VII International School-Seminar on Heavy Ion Physics, May 27 - June 1, 2002, Dubna, Russi

Measurement induced quantum-classical transition

A model of an electrical point contact coupled to a mechanical system (oscillator) is studied to simulate the dephasing effect of measurement on a quantum system. The problem is solved at zero temperature under conditions of strong non-equilibrium in the measurement apparatus. For linear coupling between the oscillator and tunneling electrons, it is found that the oscillator dynamics becomes damped, with the effective temperature determined by the voltage drop across the junction. It is demonstrated that both the quantum heating and the quantum damping of the oscillator manifest themselves in the current-voltage characteristic of the point contact.Comment: in RevTex, 1 figure, corrected notatio