Noether Theorem in Stochastic Optimal Control Problems via Contact Symmetries

We establish a generalization of the Noether theorem for stochastic optimal control problems. Exploiting the tools of jet bundles and contact geometry, we prove that from any (contact) symmetry of the Hamilton–Jacobi–Bellman equation associated with an optimal control problem it is possible to build a related local martingale. Moreover, we provide an application of the theoretical results to Merton’s optimal portfolio problem, showing that this model admits infinitely many conserved quantities in the form of local martingales.

Sharing symmetries in non-linear systems: Generalized Heisenberg–Weyl algebra on the de Sitter space-time out of the sphere S3

In this paper, we exploit the formal equivalence of the Solution Manifold of two distinct physical systems to create enough symmetries so as to characterize them by Noether Invariants, thus favoring their future quantization. In so doing, we somehow generalize the Arnold Transformation for non-necessarily linear systems. Very particularly, this algorithm applies to the case of the motion on the de Sitter space-time providing a finite-dimensional algebra generalizing the Heisenberg–Weyl algebra globally. In this case, the basic (contact) symmetry is imported from the motion of a (non-relativistic) particle on the sphere [Formula: see text].

Contact Symmetries of a Model in Optimal Investment Theory

It is generally known that Lie symmetries of differential equations can lead to a reduction of the governing equation(s), lead to exact solutions of these equations and, in the best case scenario, lead to a linearization of the original equation. In this paper, we consider a model from optimal investment theory where we show the governing equation possesses an extensive contact symmetry and, through this, we show it is linearizable. Several exact solutions are provided including a solution to a particular terminal value problem.

First-Principles Study of the Contact Resistance at 2D Metal/2D Semiconductor Heterojunctions

The high contact resistance at metal/two-dimensional (2D) semiconductor junctions is a major issue for the integration of 2D materials in nanoelectronic devices. We review here recent theoretical results on the contact resistance at lateral heterojunctions between graphene or 1T-MoS2 with 2H-MoS2 monolayers. The transport properties at these junctions are computed using density functional theory and the non-equilibrium Green’s function method. The contact resistance is found to strongly depend on the edge contact symmetry/termination at graphene/2H-MoS2 contacts, varying between about 2 × 102 and 2 × 104 Ω∙μm. This large variation is correlated to the presence or absence of dangling bond defects and/or polar bonds at the interface. On the other hand, the large computed contact resistance at pristine 1T/2H-MoS2 junctions, in the range of 3–4 × 104 Ω.μm, is related to the large electron energy barrier (about 0.8 eV) at the interface. The functionalization of the metallic 1T-MoS2 contact by various adsorbates is predicted to decrease the contact resistance by about two orders of magnitude, being very promising for device applications.

Hidden and Not So Hidden Symmetries

Hidden symmetries entered the literature in the late Eighties when it was observed that there could be gain of Lie point symmetry in the reduction of order of an ordinary differential equation. Subsequently the reverse process was also observed. Such symmetries were termed “hidden”. In each case the source of the “new” symmetry was a contact symmetry or a nonlocal symmetry, that is, a symmetry with one or more of the coefficient functions containing an integral. Recent work by Abraham-Shrauner and Govinder (2006) on the reduction of partial differential equations demonstrates that it is possible for these “hidden” symmetries to have a point origin. In this paper we show that the same phenomenon can be observed in the reduction of ordinary differential equations and in a sense loosen the interpretation of hidden symmetries.

Electroglottographic Evaluation of Gender and Vowel Effects During Modal and Vocal Fry Phonation

Two unique characteristics of vocal fry register are the occurrence of multiple opening and closing phases occurring within one vibratory cycle and a similar vocal fundamental frequency (F 0 ) between women and men. The present study tested the hypothesis that significant differences in glottal cycle symmetry exist between women and men during modal phonation, with no significant differences during vocal fry phonation. Consistent with previous studies of modal phonation, it was also hypothesized that a vowel effect would be apparent during vocal fry phonation. Five women and 5 men sustained modal and vocal fry phonations in four vowel contexts (/agr;, æ, u, i/). Vocal F 0 , duration of opening and closing phase, and contact symmetry (speed quotient) were derived from electroglottographic (EGG) waveforms. Both female and male speakers demonstrated significantly higher SQ values in vocal fry register than in their modal register, indicating a longer opening-phase duration per glottal cycle. Women demonstrated a significantly greater increase in SQ during vocal fry phonations than men, indicating greater asymmetry between opening and closing durations. The results confirmed that gender differences in vocal fold contact behavior not only exist during modal register but also during vocal fry register. No vowel effects on vocal fold contact behavior as inferred using the SQ measure were found for either modal or vocal fry registers. Possible contributing factors to multiple opening and closing phases occurring within a vibratory cycle are discussed.

VLSI-COMPATIBLE PROCESSING AND LOW-VOLTAGE OPERATION OF MULTIEMITTER Si/SiGe HETEROJUNCTION BIPOLAR TRANSISTORS

Previously we demonstrated a new class of VLSI-compatible multiemitter Si/SiGe/Si npn HBTs with enhanced logic functionality. These devices have two (or more) emitter contacts and no base contact. Given a potential difference between any two emitter contacts, one of the emitter-base junctions is forward biased and injects electrons into the base, while the other junction is reverse biased and small controlling current flows by interband tunneling. Because of emitter contact symmetry, the device possesses exclusive or functionality. Our first devices provided current gain of ~400 at room temperature, at an operating voltage of ~2 V. Here we present an improved version that operates at 1 V, as well as a multiemitter HBT fabrication sequence that is not only fully compatible with a VLSI BiCMOS process, but even saves several processing steps comapred to a standard HBT.