Abstract:
A few specific qualities of objects sharply distinguishing the objects themselves from their constituent parts are considered as emergent properties. Logical analysis shows the limitation of this point of view related to the attaching ontological content to the notion "system ". From the methodological point of view all the qualities of natural objects are emergent and their number is infinite. Emergent property seems the characteric of a researcher which considers in detail only a few properties of the things that attracted his attention. Emergent principle is a logical method of the investigation of bright "systemic qualities " based on the knowledge of the properties and relationships between the system elements as well as between the system and its environment. The key moment is the search of some "rudimantary" properties of the system components that in interaction significantly enhance the degree of their manifestation and become emergent "systemic" properties. Эмерджентными свойствами обычно считают немногочисленные особенные качества объектов, резко отличающие сами объекты от слагающих их частей. Логический анализ показывает ограниченность этой точки зрения, связанной с приданием понятию система онтологического содержания. C методологической точки зрения все качества объектов природы оказываются эмерджентными и число их бесконечно. Эмердженция оказывается характеристикой исследователя, который подробно рассматривает лишь некоторые свойства вещей, привлекшие его внимание. Принцип эмерджентности — это логический метод исследования ярких системных качеств с опорой на знание о свойствах и связях между элементами системы; между системой и объектами ее среды. Ключевым моментом является поиск неких зачаточных свойств компонентов системы, которые при взаимодействии между этими компонентами существенно усиливают степень своего проявления и становятся эмерджентными системными свойствами.

Abstract:
We study the physics of 3d supersymmetric abelian gauge theories (with small supersymmetry breaking perturbations) at finite density. Using mirror symmetry, which provides a natural generalization of the duality between the XY model and the abelian Higgs model but now including fermionic fields, we see many dynamical phenomena conjectured to be of relevance in condensed matter systems. In particular, we find examples of the emergence of a Fermi surface at low energies from hybridization of fermions localized at magnetic defects at high energies, as well as fractionalization of charged fermions into spinon-holon pairs with the concomitant appearance of emergent gauge fields. We also find dual descriptions for Fermi surfaces coupled to critical bosons, which give rise to non-Fermi liquids.

Abstract:
This is a rough transcript of talks given at the Workshop on Groups & Algebras in M Theory at Rutgers University, May 31--Jun 04, 2005. We review the basic motivation for a pre-geometric formulation of nonperturbative String/M theory, and for an underlying eleven-dimensional electric-magnetic duality, based on our current understanding of the String/M Duality Web. We explain the concept of an emerging spacetime geometry in the large N limit of a U(N) flavor matrix Lagrangian, distinguishing our proposal from generic proposals for quantum geometry, and explaining why it can incorporate curved spacetime backgrounds. We assess the significance of the extended symmetry algebra of the matrix Lagrangian, raising the question of whether our goal should be a duality covariant, or merely duality invariant, Lagrangian. We explain the conjectured isomorphism between the O(1/N) corrections in any given large N scaling limit of the matrix Lagrangian, and the corresponding alpha' corrections in a string effective Lagrangian describing some weak-coupling limit of the String/M Duality Web.

Abstract:
In this paper I develop a framework for relating dualities and emergence: two notions that are close to each other but also exclude one another. I adopt the conception of duality as 'isomorphism', cashing it out in terms of three conditions. These three conditions prompt two conceptually different ways in which a duality can be modified to make room for emergence; and I argue that this exhausts the possibilities for combining dualities and emergence (via coarse-graining). I apply this framework to gauge/gravity dualities, considering in detail three examples: AdS/CFT, Verlinde's scheme, and black holes. My main point about gauge/gravity dualities is that the theories involved, qua theories of gravity, must be background-independent. I distinguish two senses of background-independence: (i) minimalistic and (ii) extended. The former is sufficiently strong to allow for a consistent theory of quantum gravity; and AdS/CFT is background-independent on this account; while Verlinde's scheme best fits the extended sense. I argue that this extended sense should be applied with some caution: on pain of throwing the baby (general relativity) out with the bath-water (extended background-independence). Nevertheless, it is an interesting and potentially fruitful heuristic principle for quantum gravity theory construction. The interpretation of dualities is articulated in terms of: (i) epistemic and metaphysical commitments; (ii) parts vs. wholes. I then analyse the emergence of gravity in gauge/gravity dualities in terms of the two available conceptualisations of emergence; and I show how emergence in AdS/CFT and in Verlinde's scenario differ from each other. Finally, I give a novel derivation of the Bekenstein-Hawking black hole entropy formula based on Verlinde's scheme; the derivation sheds light on several aspects of Verlinde's scheme and how it compares to Bekenstein's original calculation.

Abstract:
We prove a comparison inequality between a system of independent random walkers and a system of random walkers which either interact by attracting each other -- a process which we call here the symmetric inclusion process (SIP) -- or repel each other -- a generalized version of the well-known symmetric exclusion process. As an application, new correlation inequalities are obtained for the SIP, as well as for some interacting diffusions which are used as models of heat conduction, -- the so-called Brownian momentum process, and the Brownian energy process. These inequalities are counterparts of the inequalities (in the opposite direction) for the symmetric exclusion process, showing that the SIP is a natural bosonic analogue of the symmetric exclusion process, which is fermionic. Finally, we consider a boundary driven version of the SIP for which we prove duality and then obtain correlation inequalities.

Abstract:
E-Business modelling and ebusiness systems development assumes fixed company resources, structures, and business processes. Empirical and theoretical evidence suggests that company resources and structures are emergent rather than fixed. Planning business activity in emergent contexts requires flexible ebusiness models based on better management theories and models . This paper builds and proposes a theoretical model of ebusiness systems capable of catering for emergent factors that affect business processes. Drawing on development of theories of the ‘action and design’class the Theory of Deferred Action is invoked as the base theory for the theoretical model. A theoretical model of flexible process architecture is presented by identifying its core components and their relationships, and then illustrated with exemplar flexible process architectures capable of responding to emergent factors. Managerial implications of the model are considered and the model’s generic applicability is discussed.

Abstract:
This paper develops a systematic treatment of monotonicity-based dualities for Markov processes taking values in partially ordered sets. We show that every Markov process that takes values in a finite partially ordered set and whose generator can be represented in monotone maps has a pathwise dual, which in the special setting of attractive spin systems has been discovered earlier by Gray. This dual simplifies a lot in the special case that the space is a lattice and all monotone maps satisfy an additivity condition. This leads to a unified treatment of several well-known dualities, including Siegmunds dual for processes with a totally ordered state space, duality of additive spin systems, and a duality due to Krone for the two-stage contact process. It is well-known that additive spin systems can be constructed using a graphical representation involving open paths. We show that more generally, every additive Markov process can be formulated in terms of open paths on a suitably chosen underlying space. However, in order for the process and its dual to be representable on the same underlying space, one needs to assume that the state space is a distributive lattice. In the final section, we show how our results can be generalized from finite state spaces to interacting particle systems with finite local state spaces.

Abstract:
We study the one-dimensional contact process in its quantum version using a recently proposed real space renormalisation technique for stochastic many-particle systems. Exploiting the duality and other properties of the model, we can apply the method for cells with up to 37 sites. After suitable extrapolation, we obtain exponent estimates which are comparable in accuracy with the best known in the literature.

Abstract:
We study a two-component asymmetric simple exclusion process (ASEP) that is equivalent to the ASEP with second-class particles. We prove self-duality with respect to a family of duality functions which are shown to arise from the reversible measures of the process and the symmetry of the generator under the quantum algebra $U_q[\mathfrak{gl}_3]$. We construct all invariant measures in explicit form and discuss some of their properties. We also prove a sum rule for the duality functions.

Abstract:
In this letter, the distance-duality (DD) relation is reconstructed by Gaussian process (GP) which is cosmological model-independent. Generally, the GP plays two important roles. One is to shape the $\eta$ tendency which denotes the deviation from the DD relation, the other one is to produce the luminosity-distance (LD, $D_{L}$) and the angular-diameter-distance (ADD, $D_{A}$) data at the same redshift. The shapes of $\eta$ are given out based on SNe Ia (Type Ia supernovae) data with different light-curve fitters (including MLCS2K2 and SALT2) and ADD data with different galaxy cluster morphologies (including the elliptical $\beta$ and spherical $\beta$ models). The data related to MLCS2K2 light-curve fitter have higher values of $\eta$ compared to that related to the SALT2 light-curve fitter. As for the morphology of galaxy cluster, the DD relation is favored by the elliptical one.