Virasoro constraints and flavor-topology duality in QCD

We derive Virasoro constraints for the zero momentum part of the QCD-like partition functions in the sector of topological charge v. The constraints depend on the topological charge only through the combination N-f +betav/2 where the value of the Dyson index beta is determined by the reality type of the fermions. This duality between flavor and topology is inherited by the small-mass expansion of the partition function and all spectral sum rules of inverse powers of the eigenvalues of the Dirac operator. For the special case beta =2 but arbitrary topological charge the Virasoro constraints are solved uniquely by a generalized Kontsevich model with the potential V(X) = 1/X.

On the coupling of the self-dual field to dynamical U(1) matter and its dual theory

We consider arbitrary U (1) charged matter non-minimally coupled to the self-dual field in d = 2 + 1. The coupling includes a linear and a rather general quadratic term in the self-dual field. By using both Lagragian gauge embedding and master action approaches we derive the dual Maxwell Chern-Simons-type model and show the classical equivalence between the two theories. At the quantum level the master action approach in general requires the addition of an awkward extra term to the Maxwell Chern-Simons-type theory. Only in the case of a linear coupling in the self-dual field can the extra term be dropped and we are able to establish the quantum equivalence of gauge invariant correlation functions in both theories.

Identifying financial crises in real time

Following the thermodynamic formulation of a multifractal measure that was shown to enable the detection of large fluctuations at an early stage, here we propose a new index which permits us to distinguish events like financial crises in real time. We calculate the partition function from which we can obtain thermodynamic quantities analogous to the free energy and specific heat. The index is defined as the normalized energy variation and it can be used to study the behavior of stochastic time series, such as financial market daily data. Famous financial market crashes-Black Thursday (1929), Black Monday (1987) and the subprime crisis (2008)-are identified with clear and robust results. The method is also applied to the market fluctuations of 2011. From these results it appears as if the apparent crisis of 2011 is of a different nature to the other three. We also show that the analysis has forecasting capabilities. © 2012 Elsevier B.V. All rights reserved.

Thermal phase transition for some spin-boson models

In this work we study two different spin-boson models. Such models are generalizations of the Dicke model, it means they describe systems of N identical two-level atoms coupled to a single-mode quantized bosonic field, assuming the rotating wave approximation. In the first model, we consider the wavelength of the bosonic field to be of the order of the linear dimension of the material composed of the atoms, therefore we consider the spatial sinusoidal form of the bosonic field. The second model is the Thompson model, where we consider the presence of phonons in the material composed of the atoms. We study finite temperature properties of the models using the path integral approach and functional methods. In the thermodynamic limit, N→∞, the systems exhibit phase transitions from normal to superradiant phase at some critical values of temperature and coupling constant. We find the asymptotic behavior of the partition functions and the collective spectrums of the systems in the normal and the superradiant phases. We observe that the collective spectrums have zero energy values in the superradiant phases, corresponding to the Goldstone mode associated to the continuous symmetry breaking of the models. Our analysis and results are valid in the limit of zero temperature β→∞, where the models exhibit quantum phase transitions. © 2013 Elsevier B.V. All rights reserved.

Hilbert space of curved βγ systems on quadric cones

We clarify the structure of the Hilbert space of curved βγ systems defined by a quadratic constraint. The constraint is studied using intrinsic and BRST methods, and their partition functions are shown to agree. The quantum BRST cohomology is non-empty only at ghost numbers 0 and 1, and there is a one-to-one mapping between these two sectors. In the intrinsic description, the ghost number 1 operators correspond to the ones that are not globally defined on the constrained surface. Extension of the results to the pure spinor superstring is discussed in a separate work.

ANKLE IMPEDANCE AND ANKLE ANGLES DURING STEP TURN AND STRAIGHT WALK: IMPLICATIONS FOR THE DESIGN OF A STEERABLE ANKLE-FOOT PROSTHETIC ROBOT

During locomotion, turning is a common and recurring event which is largely neglected in the current state-of-the-art ankle-foot prostheses, forcing amputees to use different steering mechanisms for turning, compared to non-amputees. A better understanding of the complexities surrounding lower limb prostheses will lead to increased health and well-being of amputees. The aim of this research is to develop a steerable ankle-foot prosthesis that mimics the human ankle mechanical properties. Experiments were developed to estimate the mechanical impedance of the ankle and the ankles angles during straight walk and step turn. Next, this information was used in the design of a prototype, powered steerable ankle-foot prosthesis with two controllable degrees of freedom. One of the possible approaches in design of the prosthetic robots is to use the human joints’ parameters, especially their impedance. A series of experiments were conducted to estimate the stochastic mechanical impedance of the human ankle when muscles were fully relaxed and co-contracting antagonistically. A rehabilitation robot for the ankle, Anklebot, was employed to provide torque perturbations to the ankle. The experiments were performed in two different configurations, one with relaxed muscles, and one with 10% of maximum voluntary contraction (MVC). Surface electromyography (sEMG) was used to monitor muscle activation levels and these sEMG signals were displayed to subjects who attempted to maintain them constant. Time histories of ankle torques and angles in the lateral/medial (LM) directions, inversion-eversion (IE), and dorsiflexionplantarflexion (DP) were recorded. Linear time-invariant transfer functions between the measured torques and angles were estimated providing an estimate of ankle mechanical impedance. High coherence was observed over a frequency range up to 30 Hz. The main effect of muscle activation was to increase the magnitude of ankle mechanical impedance in all degrees of freedom of the ankle. Another experiment compared the three-dimensional angles of the ankle during step turn and straight walking. These angles were measured to be used for developing the control strategy of the ankle-foot prosthesis. An infrared camera system was used to track the trajectories and angles of the foot and leg. The combined phases of heel strike and loading response, mid stance, and terminal stance and pre-swing were determined and used to measure the average angles at each combined phase. The Range of motion (ROM) in IE increased during turning while ML rotation decreased and DP changed the least. During the turning step, ankle displacement in DP started with similar angles to straight walk and progressively showed less plantarflexion. In IE, the ankle showed increased inversion leaning the body toward the inside of the turn. ML rotation initiated with an increased medial rotation during the step turn relative to the straight walk transitioning to increased lateral rotation at the toe off. A prototype ankle-foot prosthesis capable of controlling both DP and IE using a cable driven mechanism was developed and assessed as part of a feasibility study. The design is capable of reproducing the angles required for straight walk and step turn; generates 712N of lifting force in plantarflexion, and shows passive stiffness comparable to a nonload bearing ankle impedance. To evaluate the performance of the ankle-foot prosthesis, a circular treadmill was developed to mimic human gait during steering. Preliminary results show that the device can appropriately simulate human gait with loading and unloading the ankle joint during the gait in circular paths.

(Non)-Dissipative Hydrodynamics on Embedded Surfaces

We construct the theory of dissipative hydrodynamics of uncharged fluids living on embedded space-time surfaces to first order in a derivative expansion in the case of codimension-1 surfaces (including fluid membranes) and the theory of non-dissipative hydrodynamics to second order in a derivative expansion in the case of codimension higher than one under the assumption of no angular momenta in transverse directions to the surface. This construction includes the elastic degrees of freedom, and hence the corresponding transport coefficients, that take into account transverse fluctuations of the geometry where the fluid lives. Requiring the second law of thermodynamics to be satisfied leads us to conclude that in the case of codimension-1 surfaces the stress-energy tensor is characterized by 2 hydrodynamic and 1 elastic independent transport coefficient to first order in the expansion while for codimension higher than one, and for non-dissipative flows, the stress-energy tensor is characterized by 7 hydrodynamic and 3 elastic independent transport coefficients to second order in the expansion. Furthermore, the constraints imposed between the stress-energy tensor, the bending moment and the entropy current of the fluid by these extra non-dissipative contributions are fully captured by equilibrium partition functions. This analysis constrains the Young modulus which can be measured from gravity by elastically perturbing black branes.

Bargaining for power and information : an experimental and theoretical analysis of the interaction between institutions, externalities and adverse selection

Bargaining is the building block of many economic interactions, ranging from bilateral to multilateral encounters and from situations in which the actors are individuals to negotiations between firms or countries. In all these settings, economists have been intrigued for a long time by the fact that some projects, trades or agreements are not realized even though they are mutually beneficial. On the one hand, this has been explained by incomplete information. A firm may not be willing to offer a wage that is acceptable to a qualified worker, because it knows that there are also unqualified workers and cannot distinguish between the two types. This phenomenon is known as adverse selection. On the other hand, it has been argued that even with complete information, the presence of externalities may impede efficient outcomes. To see this, consider the example of climate change. If a subset of countries agrees to curb emissions, non-participant regions benefit from the signatories’ efforts without incurring costs. These free riding opportunities give rise to incentives to strategically improve ones bargaining power that work against the formation of a global agreement. This thesis is concerned with extending our understanding of both factors, adverse selection and externalities. The findings are based on empirical evidence from original laboratory experiments as well as game theoretic modeling. On a very general note, it is demonstrated that the institutions through which agents interact matter to a large extent. Insights are provided about which institutions we should expect to perform better than others, at least in terms of aggregate welfare. Chapters 1 and 2 focus on the problem of adverse selection. Effective operation of markets and other institutions often depends on good information transmission properties. In terms of the example introduced above, a firm is only willing to offer high wages if it receives enough positive signals about the worker’s quality during the application and wage bargaining process. In Chapter 1, it will be shown that repeated interaction coupled with time costs facilitates information transmission. By making the wage bargaining process costly for the worker, the firm is able to obtain more accurate information about the worker’s type. The cost could be pure time cost from delaying agreement or cost of effort arising from a multi-step interviewing process. In Chapter 2, I abstract from time cost and show that communication can play a similar role. The simple fact that a worker states to be of high quality may be informative. In Chapter 3, the focus is on a different source of inefficiency. Agents strive for bargaining power and thus may be motivated by incentives that are at odds with the socially efficient outcome. I have already mentioned the example of climate change. Other examples are coalitions within committees that are formed to secure voting power to block outcomes or groups that commit to different technological standards although a single standard would be optimal (e.g. the format war between HD and BlueRay). It will be shown that such inefficiencies are directly linked to the presence of externalities and a certain degree of irreversibility in actions. I now discuss the three articles in more detail. In Chapter 1, Olivier Bochet and I study a simple bilateral bargaining institution that eliminates trade failures arising from incomplete information. In this setting, a buyer makes offers to a seller in order to acquire a good. Whenever an offer is rejected by the seller, the buyer may submit a further offer. Bargaining is costly, because both parties suffer a (small) time cost after any rejection. The difficulties arise, because the good can be of low or high quality and the quality of the good is only known to the seller. Indeed, without the possibility to make repeated offers, it is too risky for the buyer to offer prices that allow for trade of high quality goods. When allowing for repeated offers, however, at equilibrium both types of goods trade with probability one. We provide an experimental test of these predictions. Buyers gather information about sellers using specific price offers and rates of trade are high, much as the model’s qualitative predictions. We also observe a persistent over-delay before trade occurs, and this mitigates efficiency substantially. Possible channels for over-delay are identified in the form of two behavioral assumptions missing from the standard model, loss aversion (buyers) and haggling (sellers), which reconcile the data with the theoretical predictions. Chapter 2 also studies adverse selection, but interaction between buyers and sellers now takes place within a market rather than isolated pairs. Remarkably, in a market it suffices to let agents communicate in a very simple manner to mitigate trade failures. The key insight is that better informed agents (sellers) are willing to truthfully reveal their private information, because by doing so they are able to reduce search frictions and attract more buyers. Behavior observed in the experimental sessions closely follows the theoretical predictions. As a consequence, costless and non-binding communication (cheap talk) significantly raises rates of trade and welfare. Previous experiments have documented that cheap talk alleviates inefficiencies due to asymmetric information. These findings are explained by pro-social preferences and lie aversion. I use appropriate control treatments to show that such consideration play only a minor role in our market. Instead, the experiment highlights the ability to organize markets as a new channel through which communication can facilitate trade in the presence of private information. In Chapter 3, I theoretically explore coalition formation via multilateral bargaining under complete information. The environment studied is extremely rich in the sense that the model allows for all kinds of externalities. This is achieved by using so-called partition functions, which pin down a coalitional worth for each possible coalition in each possible coalition structure. It is found that although binding agreements can be written, efficiency is not guaranteed, because the negotiation process is inherently non-cooperative. The prospects of cooperation are shown to crucially depend on i) the degree to which players can renegotiate and gradually build up agreements and ii) the absence of a certain type of externalities that can loosely be described as incentives to free ride. Moreover, the willingness to concede bargaining power is identified as a novel reason for gradualism. Another key contribution of the study is that it identifies a strong connection between the Core, one of the most important concepts in cooperative game theory, and the set of environments for which efficiency is attained even without renegotiation.

Topics in equilibrium and nonequilibrium thermodynamics: computing crystalline free energies and engineering Maxwell’s demon.

This dissertation covers two separate topics in statistical physics. The first part of the dissertation focuses on computational methods of obtaining the free energies (or partition functions) of crystalline solids. We describe a method to compute the Helmholtz free energy of a crystalline solid by direct evaluation of the partition function. In the many-dimensional conformation space of all possible arrangements of N particles inside a periodic box, the energy landscape consists of localized islands corresponding to different solid phases. Calculating the partition function for a specific phase involves integrating over the corresponding island. Introducing a natural order parameter that quantifies the net displacement of particles from lattices sites, we write the partition function in terms of a one-dimensional integral along the order parameter, and evaluate this integral using umbrella sampling. We validate the method by computing free energies of both face-centered cubic (FCC) and hexagonal close-packed (HCP) hard sphere crystals with a precision of $10^{-5}k_BT$ per particle. In developing the numerical method, we find several scaling properties of crystalline solids in the thermodynamic limit. Using these scaling properties, we derive an explicit asymptotic formula for the free energy per particle in the thermodynamic limit. In addition, we describe several changes of coordinates that can be used to separate internal degrees of freedom from external, translational degrees of freedom. The second part of the dissertation focuses on engineering idealized physical devices that work as Maxwell's demon. We describe two autonomous mechanical devices that extract energy from a single heat bath and convert it into work, while writing information onto memory registers. Additionally, both devices can operate as Landauer's eraser, namely they can erase information from a memory register, while energy is dissipated into the heat bath. The phase diagrams and the efficiencies of the two models are solved and analyzed. These two models provide concrete physical illustrations of the thermodynamic consequences of information processing.

Equality of P-partition Generating Functions

To every partially ordered set (poset), one can associate a generating function, known as the P-partition generating function. We find necessary conditions and sufficient conditions for two posets to have the same P-partition generating function. We define the notion of a jump sequence for a labeled poset and show that having equal jumpsequences is a necessary condition for generating function equality. We also develop multiple ways of modifying posets that preserve generating function equality. Finally, we are able to give a complete classification of equalities among partially ordered setswith exactly two linear extensions.

Intestinal microbes affect phenotypes and functions of invariant natural killer T cells in mice

Invariant natural killer T (iNKT) cells undergo canonical, Vα14-Jα18 rearrangement of the T-cell receptor (TCR) in mice; this form of the TCR recognizes glycolipids presented by CD1d. iNKT cells mediate many different immune reactions. Their constitutive activated and memory phenotype and rapid initiation of effector functions after stimulation indicate previous antigen-specific stimulation. However, little is known about this process. We investigated whether symbiotic microbes can determine the activated phenotype and function of iNKT cells.

Kernels and Designs for Modelling Invariant Functions: From Group Invariance to Additivity

We focus on kernels incorporating different kinds of prior knowledge on functions to be approximated by Kriging. A recent result on random fields with paths invariant under a group action is generalised to combinations of composition operators, and a characterisation of kernels leading to random fields with additive paths is obtained as a corollary. A discussion follows on some implications on design of experiments, and it is shown in the case of additive kernels that the so-called class of “axis designs” outperforms Latin hypercubes in terms of the IMSE criterion.

Invariant Functions on Neil Parabola in Cn

2000 Mathematics Subject Classification: Primary 32F45.