Some Heuristic Semiclassical Derivations of the Planck Length, the Hawking Effect and the Unruh Effect

The formulae for Planck length, Hawking temperature and Unruh-Davies temperature are derived by using only laws of classical physics together with the Heisenberg principle. Besides, it is shown how the Hawking relation can be deduced from the Unruh relation by means of the principle of equivalence; the deep link between Hawking effect and Unruh effect is in this way clarified.Comment: LaTex file, 6 pages, no figure

Born's rule from measurements of classical signals by threshold detectors which are properly calibrated

The very old problem of the statistical content of quantum mechanics (QM) is studied in a novel framework. The Born's rule (one of the basic postulates of QM) is derived from theory of classical random signals. We present a measurement scheme which transforms continuous signals into discrete clicks and reproduces the Born's rule. This is the sheme of threshold type detection. Calibration of detectors plays a crucial role.Comment: The problem of double clicks is resolved; hence, one can proceed in purely wave framework, i.e., the wave-partcile duality has been resolved in favor of the wave picture of prequantum realit

Exponential Separation of Quantum and Classical Online Space Complexity

Although quantum algorithms realizing an exponential time speed-up over the best known classical algorithms exist, no quantum algorithm is known performing computation using less space resources than classical algorithms. In this paper, we study, for the first time explicitly, space-bounded quantum algorithms for computational problems where the input is given not as a whole, but bit by bit. We show that there exist such problems that a quantum computer can solve using exponentially less work space than a classical computer. More precisely, we introduce a very natural and simple model of a space-bounded quantum online machine and prove an exponential separation of classical and quantum online space complexity, in the bounded-error setting and for a total language. The language we consider is inspired by a communication problem (the set intersection function) that Buhrman, Cleve and Wigderson used to show an almost quadratic separation of quantum and classical bounded-error communication complexity. We prove that, in the framework of online space complexity, the separation becomes exponential.Comment: 13 pages. v3: minor change

In vivo manipulation of the extracellular matrix induces vascular regression in a basal chordate.

We investigated the physical role of the extracellular matrix (ECM) in vascular homeostasis in the basal chordate Botryllus schlosseri, which has a large, transparent, extracorporeal vascular network encompassing an area >100 cm2 We found that the collagen cross-linking enzyme lysyl oxidase is expressed in all vascular cells and that in vivo inhibition using β-aminopropionitrile (BAPN) caused a rapid, global regression of the entire network, with some vessels regressing >10 mm within 16 h. BAPN treatment changed the ultrastructure of collagen fibers in the vessel basement membrane, and the kinetics of regression were dose dependent. Pharmacological inhibition of both focal adhesion kinase (FAK) and Raf also induced regression, and levels of phosphorylated FAK in vascular cells decreased during BAPN treatment and FAK inhibition but not Raf inhibition, suggesting that physical changes in the vessel ECM are detected via canonical integrin signaling pathways. Regression is driven by apoptosis and extrusion of cells through the basal lamina, which are then engulfed by blood-borne phagocytes. Extrusion and regression occurred in a coordinated manner that maintained vessel integrity, with no loss of barrier function. This suggests the presence of regulatory mechanisms linking physical changes to a homeostatic, tissue-level response

New Results in Sasaki-Einstein Geometry

This article is a summary of some of the author's work on Sasaki-Einstein geometry. A rather general conjecture in string theory known as the AdS/CFT correspondence relates Sasaki-Einstein geometry, in low dimensions, to superconformal field theory; properties of the latter are therefore reflected in the former, and vice versa. Despite this physical motivation, many recent results are of independent geometrical interest, and are described here in purely mathematical terms: explicit constructions of infinite families of both quasi-regular and irregular Sasaki-Einstein metrics; toric Sasakian geometry; an extremal problem that determines the Reeb vector field for, and hence also the volume of, a Sasaki-Einstein manifold; and finally, obstructions to the existence of Sasaki-Einstein metrics. Some of these results also provide new insights into Kahler geometry, and in particular new obstructions to the existence of Kahler-Einstein metrics on Fano orbifolds.Comment: 31 pages, no figures. Invited contribution to the proceedings of the conference "Riemannian Topology: Geometric Structures on Manifolds"; minor typos corrected, reference added; published version; Riemannian Topology and Geometric Structures on Manifolds (Progress in Mathematics), Birkhauser (Nov 2008

Optimal liability sharing and court errors: an exploratory analysis

We focus in this paper on the effects of court errors on the optimal sharing of liability between firms and financiers, as an environmental policy instrument. Using a structural model of the interactions between firms, financial institutions, governments and courts we show, through numerical simulations, the distortions in liability sharing between firms and financiers that the imperfect implementation of government policies implies. We consider in particular the role played by the efficiency of the courts in avoiding Type I (finding an innocent firm guilty of inappropriate care) and Type II (finding a guilty firm innocent of inappropriate care) errors. This role is considered in a context where liability sharing is already distorted (when compared with first best values) due not only to the courts' own imperfect assessment of safety care levels exerted by firm but also to the presence of moral hazard and adverse selection in financial contracting, as well as of noncongruence of objectives between firms and financiers on the one hand and social welfare maximization on the other. Our results indicate that an increase in the efficiency of the court system in avoiding errors raises safety care levels, thereby reducing the probability of accident, and allowing the social welfare maximizing government to impose a lower liability [higher] share for firms [financiers] as well as a lower standard level of care

Duel and sweep algorithm for order-preserving pattern matching

Given a text $T$ and a pattern $P$ over alphabet $\Sigma$, the classic exact matching problem searches for all occurrences of pattern $P$ in text $T$. Unlike exact matching problem, order-preserving pattern matching (OPPM) considers the relative order of elements, rather than their real values. In this paper, we propose an efficient algorithm for OPPM problem using the "duel-and-sweep" paradigm. Our algorithm runs in $O(n + m\log m)$ time in general and $O(n + m)$ time under an assumption that the characters in a string can be sorted in linear time with respect to the string size. We also perform experiments and show that our algorithm is faster that KMP-based algorithm. Last, we introduce the two-dimensional order preserved pattern matching and give a duel and sweep algorithm that runs in $O(n^2)$ time for duel stage and $O(n^2 m)$ time for sweeping time with $O(m^3)$ preprocessing time.Comment: 13 pages, 5 figure

Derivation of the Planck Spectrum for Relativistic Classical Scalar Radiation from Thermal Equilibrium in an Accelerating Frame

The Planck spectrum of thermal scalar radiation is derived suggestively within classical physics by the use of an accelerating coordinate frame. The derivation has an analogue in Boltzmann's derivation of the Maxwell velocity distribution for thermal particle velocities by considering the thermal equilibrium of noninteracting particles in a uniform gravitational field. For the case of radiation, the gravitational field is provided by the acceleration of a Rindler frame through Minkowski spacetime. Classical zero-point radiation and relativistic physics enter in an essential way in the derivation which is based upon the behavior of free radiation fields and the assumption that the field correlation functions contain but a single correlation time in thermal equilibrium. The work has connections with the thermal effects of acceleration found in relativistic quantum field theory.Comment: 23 page