153 research outputs found
Quantum-classical tradeoffs and multi-controlled quantum gate decompositions in variational algorithms
Quantum algorithms for unconstrained optimization problems, such as the
Quantum Approximate Optimization Algorithm (QAOA), have been proposed as
interesting near-term algorithms which operate under a hybrid quantum-classical
execution model. Recent work has shown that the QAOA can also be applied to
constrained combinatorial optimization problems by incorporating the problem
constraints within the design of the variational ansatz - often resulting in
quantum circuits containing many multi-controlled gate operations. This paper
investigates potential resource tradeoffs for the QAOA when applied to the
particular constrained optimization problem of Maximum Independent Set. We
consider three variants of the QAOA which make different tradeoffs between the
number of classical parameters, quantum gates, and iterations of classical
optimization. We also study the quantum cost of decomposing the QAOA circuits
on hardware which may support different qubit technologies and native gate
sets, and compare the different algorithms using the gate decomposition score
which combines the fidelity of the gate operations with the efficiency of the
decomposition into a single metric. We find that all three QAOA variants can
attain similar performance but the classical and quantum resource costs may
vary greatly between them.Comment: 17 pages, 8 figures, 5 table
The Network Analysis of Urban Streets: A Primal Approach
The network metaphor in the analysis of urban and territorial cases has a
long tradition especially in transportation/land-use planning and economic
geography. More recently, urban design has brought its contribution by means of
the "space syntax" methodology. All these approaches, though under different
terms like accessibility, proximity, integration,connectivity, cost or effort,
focus on the idea that some places (or streets) are more important than others
because they are more central. The study of centrality in complex
systems,however, originated in other scientific areas, namely in structural
sociology, well before its use in urban studies; moreover, as a structural
property of the system, centrality has never been extensively investigated
metrically in geographic networks as it has been topologically in a wide range
of other relational networks like social, biological or technological. After
two previous works on some structural properties of the dual and primal graph
representations of urban street networks (Porta et al. cond-mat/0411241;
Crucitti et al. physics/0504163), in this paper we provide an in-depth
investigation of centrality in the primal approach as compared to the dual one,
with a special focus on potentials for urban design.Comment: 19 page, 4 figures. Paper related to the paper "The Network Analysis
of Urban Streets: A Dual Approach" cond-mat/041124
Two-state Bose-Hubbard model in the hard-core boson limit
Phase transition into the phase with Bose-Einstein (BE) condensate in the
two-band Bose-Hubbard model with the particle hopping in the excited band only
is investigated. Instability connected with such a transition (which appears at
excitation energies , where is
the particle hopping parameter) is considered. The re-entrant behaviour of
spinodales is revealed in the hard-core boson limit in the region of positive
values of chemical potential. It is found that the order of the phase
transition undergoes a change in this case and becomes the first one; the
re-entrant transition into the normal phase does not take place in reality.
First order phase transitions also exist at negative values of (under
the condition ).
At the phase transition mostly remains to be of the second order. The
behaviour of the BE-condensate order parameter is analyzed, the
and phase diagrams are built and localizations of
tricritical points are established. The conditions are found at which the
separation on the normal phase and the phase with the BE condensate takes
place.Comment: 14 pages, 12 figure
A Study of the United States Influence on German Eugenics.
This thesis is a study of the influence and effects that the United States had upon Germany from the rise of eugenics to its fall following the end of World War II. There are three stages to this study. First, I examine the rise of eugenics in the United States from its inception to the end of World War I and the influence it had upon Germany. Then I examine the interwar era along with the popularization of eugenics within both countries before concluding with the Second World War and post war era.
My thesis focuses on both the active and passive influences that the United States had upon German eugenics and racial hygiene in the twentieth century. This study uses a wide range of primary and secondary sources. Many of the authors are experts in their field while the visuals are a window into understanding how eugenics was spread to the public
Robustness of Randomized Rumour Spreading
In this work we consider three well-studied broadcast protocols: Push, Pull
and Push&Pull. A key property of all these models, which is also an important
reason for their popularity, is that they are presumed to be very robust, since
they are simple, randomized, and, crucially, do not utilize explicitly the
global structure of the underlying graph. While sporadic results exist, there
has been no systematic theoretical treatment quantifying the robustness of
these models. Here we investigate this question with respect to two orthogonal
aspects: (adversarial) modifications of the underlying graph and message
transmission failures.
We explore in particular the following notion of Local Resilience: beginning
with a graph, we investigate up to which fraction of the edges an adversary has
to be allowed to delete at each vertex, so that the protocols need
significantly more rounds to broadcast the information. Our main findings
establish a separation among the three models. It turns out that Pull is robust
with respect to all parameters that we consider. On the other hand, Push may
slow down significantly, even if the adversary is allowed to modify the degrees
of the vertices by an arbitrarily small positive fraction only. Finally,
Push&Pull is robust when no message transmission failures are considered,
otherwise it may be slowed down.
On the technical side, we develop two novel methods for the analysis of
randomized rumour spreading protocols. First, we exploit the notion of
self-bounding functions to facilitate significantly the round-based analysis:
we show that for any graph the variance of the growth of informed vertices is
bounded by its expectation, so that concentration results follow immediately.
Second, in order to control adversarial modifications of the graph we make use
of a powerful tool from extremal graph theory, namely Szemer\`edi's Regularity
Lemma.Comment: version 2: more thorough literature revie
Environmental Demands and the Emergence of Social Structure: Technological Dynamism and Interorganizational Network Forms
This study investigates the origins of variation in the structures of interorganizational networks across industries. We combine empirical analyses of existing interorganizational networks with an agent-based simulation model of network emergence. Our insights are twofold. First, we find that differences in technological dynamism across industries and the concomitant demands for value creation engender variations in firms’ collaborative behaviors. On average, firms in technologically dynamic industries pursue more open ego networks, which fosters access to new and diverse resources that help sustain continuous innovation. In contrast, firms in technologically stable industries on average pursue more closed ego networks, which fosters reliable collaboration and helps preserve existing resources. Second, we show that because of the observed cross-industry differences in firms’ collaborative behaviors, the emergent industry-wide networks take on distinct structural forms. Technologically stable industries feature clan networks, characterized by low network connectedness and rather strong community structures. Technologically dynamic industries, in turn, feature community networks, characterized by high network connectedness and medium-to-strong community structures. Convention networks, which feature high network connectedness and weak community structures, were not evident among the empirical networks we examined. Taken together, our findings advance an environmental contingency theory of network formation.http://deepblue.lib.umich.edu/bitstream/2027.42/112051/1/1282_Sytch.pd
Strategic Voting and Social Networks
With the ever increasing ubiquity of social networks in our everyday lives, comes an increasing urgency for us to understand their impact on human behavior. Social networks quantify the ways in which we communicate with each other, and therefore shape the flow of information through the community. It is this same flow of information that we utilize to make sound, strategic decisions. This thesis focuses on one particular type of decisions: voting. When a community engages in voting, it is soliciting the opinions of its members, who present it in the form of a ballot. The community may then choose a course of action based on the submitted ballots. Individual voters, however, are under no obligation to submit sincere ballots that accurately reflects their opinions; they may instead submit a strategic ballot in hopes of affecting the election's outcome to their advantage. This thesis examines the interplay between social network structure and strategic voting behavior. In particular, we will explore how social network structure affects the flow of information through a population, and thereby affect the strategic behavior of voters, and ultimately, the outcomes of elections.
We will begin by considering how network structure affects information propagation. This work builds upon the rich body of literature called opinion dynamics by proposing a model for skeptical agents --- agents that distrust other agents for holding opinions that differ too wildly from their own. We show that network structure is one of several factors that affects the degree of penetration that radical opinions can achieve through the community. Next, we propose a model for strategic voting in social networks, where voters are self-interested and rational, but may only use the limited information available through their social network contacts to formulate strategic ballots. In particular, we study the ``Echo Chamber Effect'', the tendency for humans to favor connections with similar people, and show that it leads to the election of less suitable candidates. We also extend this voter model by using boundedly-rational heuristics to scale up our simulations to larger populations. We propose a general framework for voting agents embedded in social networks, and show that our heuristic models can demonstrate a variation of the ``Micromega Law'' which relates the popularity of smaller parties to the size of the population. Finally, we examine another avenue for strategic behavior: choosing when to cast your vote. We propose a type of voting mechanism called ``Sticker Voting'', where voters cast ballots by placing stickers on their favored alternatives, thereby publicly and irrevocably declaring their support. We present a complete analysis of several simple instances of the Sticker Voting game and discuss how our results reflect human voting behavior
Forcing a countable structure to belong to the ground model
Suppose that is a forcing notion, is a language (in ),
a -name such that " is a countable
-structure". In the product , there are names
such that for any generic filter over , and
. Zapletal asked whether or not implies that there is some
such that . We answer this negatively and
discuss related issues
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