1,216 research outputs found
Fractal dimension of domain walls in two-dimensional Ising spin glasses
We study domain walls in 2d Ising spin glasses in terms of a minimum-weight
path problem. Using this approach, large systems can be treated exactly. Our
focus is on the fractal dimension of domain walls, which describes via
\simL^{d_f} the growth of the average domain-wall length with %%
systems size . %% 20.07.07 OM %% Exploring systems up to L=320 we
yield for the case of Gaussian disorder, i.e. a much higher
accuracy compared to previous studies. For the case of bimodal disorder, where
many equivalent domain walls exist due to the degeneracy of this model, we
obtain a true lower bound and a (lower) estimate
as upper bound. Furthermore, we study the distributions of the domain-wall
lengths. Their scaling with system size can be described also only by the
exponent , i.e. the distributions are monofractal. Finally, we investigate
the growth of the domain-wall width with system size (``roughness'') and find a
linear behavior.Comment: 8 pages, 8 figures, submitted to Phys. Rev. B; v2: shortened versio
Ratio-Balanced Maximum Flows
When a loan is approved for a person or company, the bank is subject to \emph{credit risk}; the risk that the lender defaults. To mitigate this risk, a bank will require some form of \emph{security}, which will be collected if the lender defaults. Accounts can be secured by several securities and a security can be used for several accounts. The goal is to fractionally assign the securities to the accounts so as to balance the risk. This situation can be modelled by a bipartite graph. We have a set of securities and a set of accounts. Each security has a \emph{value} and each account has an \emph{exposure} . If a security can be used to secure an account , we have an edge from to . Let be part of security 's value used to secure account . We are searching for a maximum flow that send at most units out of node and at most units into node . Then is the unsecured part of account . We are searching for the maximum flow that minimizes
Design and Synthesis of Custom Styryl BODIPY Dyes for Bimodal Imaging
Innovation towards new agents for combined positron emission tomography/optical imaging is of significance for making advances in patient diagnosis. As of recent, boron-dipyrromethene (4,4-difluoro-4-bora-3a,4a-diaza-s-indacene, BODIPY) dyes have shown promise as bimodal imaging agents serving as a fluorescent tag with capability to act as a fluorine-18 radiotracer. However, due the sensitivity of these molecules their chemical transformations are poorly understood. In this thesis, I address the synthetic challenge of near-infrared, “clickable” BODIPY dyes with complex functionality in order to identify reliable syntheses.
Early investigation was concentrated on understanding the intricacies of BODIPY synthesis; in particular, the low yielding incorporation of boron difluoride. Conventional one-pot procedures were revised, and it was found that isolating the dipyrromethene scaffold followed by boron complexation improved the yield overall. In addition, aqueous work up procedures were modified to avoid the decomplexation of boron difluoride from the BODIPY product by vacuum-assisted removal of excess boron trifluoride. Robust synthetic procedures were established to afford the azido- functionalized BODIPY, which is valuable for tagging novel BODIPY dyes to disease-targeting vectors using “Click Chemistry”.
The latter of the thesis focused on improving the water-solubility of the conjugated BODIPY dyes by addition of ionizable groups which can also partake in hydrogen bonding, making them suitable for biological application. It was found that the BODIPY molecule could not withstand ester hydrolysis conditions needed to produce diacid BODIPY derivatives. Alternatively, a Knoevenagel-like condensation provided two near-infrared BODIPY dyes, one bearing dihydroxy (phenolic) functionality demonstrating partial water-solubility. The dyes were characterized as long wavelength dyes to compliment future Price group studies
Transit Node Routing Reconsidered
Transit Node Routing (TNR) is a fast and exact distance oracle for road
networks. We show several new results for TNR. First, we give a surprisingly
simple implementation fully based on Contraction Hierarchies that speeds up
preprocessing by an order of magnitude approaching the time for just finding a
CH (which alone has two orders of magnitude larger query time). We also develop
a very effective purely graph theoretical locality filter without any
compromise in query times. Finally, we show that a specialization to the online
many-to-one (or one-to-many) shortest path further speeds up query time by an
order of magnitude. This variant even has better query time than the fastest
known previous methods which need much more space.Comment: 19 pages, submitted to SEA'201
Nash Social Welfare for 2-value Instances
We study the problem of allocating a set of indivisible goods among agents with 2-value additive valuations. Our goal is to find an allocation with maximum Nash social welfare, i.e., the geometric mean of the valuations of the agents. We give a polynomial-time algorithm to find a Nash social welfare maximizing allocation when the valuation functions are integrally 2-valued, i.e., each agent has a value either or for each good, for some positive integer . We then extend our algorithm to find a better approximation factor for general 2-value instances
EFX Allocations: Simplifications and Improvements
The existence of EFX allocations is a fundamental open problem in discretefair division. Given a set of agents and indivisible goods, the goal is todetermine the existence of an allocation where no agent envies anotherfollowing the removal of any single good from the other agent's bundle. Sincethe general problem has been illusive, progress is made on two fronts: proving existence when the number of agents is small, proving existenceof relaxations of EFX. In this paper, we improve results on both fronts (andsimplify in one of the cases). We prove the existence of EFX allocations with three agents, restricting onlyone agent to have an MMS-feasible valuation function (a strict generalizationof nice-cancelable valuation functions introduced by Berger et al. whichsubsumes additive, budget-additive and unit demand valuation functions). Theother agents may have any monotone valuation functions. Our proof technique issignificantly simpler and shorter than the proof by Chaudhury et al. onexistence of EFX allocations when there are three agents with additivevaluation functions and therefore more accessible. Secondly, we consider relaxations of EFX allocations, namely, approximate-EFXallocations and EFX allocations with few unallocated goods (charity). Chaudhuryet al. showed the existence of -EFX allocation with charity by establishing a connection to aproblem in extremal combinatorics. We improve their result and prove theexistence of -EFX allocations with charity. In fact, some of our techniques can be usedto prove improved upper-bounds on a problem in zero-sum combinatoricsintroduced by Alon and Krivelevich.<br
One-variable word equations in linear time
In this paper we consider word equations with one variable (and arbitrary
many appearances of it). A recent technique of recompression, which is
applicable to general word equations, is shown to be suitable also in this
case. While in general case it is non-deterministic, it determinises in case of
one variable and the obtained running time is O(n + #_X log n), where #_X is
the number of appearances of the variable in the equation. This matches the
previously-best algorithm due to D\k{a}browski and Plandowski. Then, using a
couple of heuristics as well as more detailed time analysis the running time is
lowered to O(n) in RAM model. Unfortunately no new properties of solutions are
shown.Comment: submitted to a journal, general overhaul over the previous versio
Domain-Wall Energies and Magnetization of the Two-Dimensional Random-Bond Ising Model
We study ground-state properties of the two-dimensional random-bond Ising
model with couplings having a concentration of antiferromagnetic
and of ferromagnetic bonds. We apply an exact matching algorithm which
enables us the study of systems with linear dimension up to 700. We study
the behavior of the domain-wall energies and of the magnetization. We find that
the paramagnet-ferromagnet transition occurs at compared to
the concentration at the Nishimory point, which means that the
phase diagram of the model exhibits a reentrance. Furthermore, we find no
indications for an (intermediate) spin-glass ordering at finite temperature.Comment: 7 pages, 12 figures, revTe
Ground-State and Domain-Wall Energies in the Spin-Glass Region of the 2D Random-Bond Ising Model
The statistics of the ground-state and domain-wall energies for the
two-dimensional random-bond Ising model on square lattices with independent,
identically distributed bonds of probability of and of
are studied. We are able to consider large samples of up to
spins by using sophisticated matching algorithms. We study
systems, but we also consider samples, for different aspect ratios
. We find that the scaling behavior of the ground-state energy and
its sample-to-sample fluctuations inside the spin-glass region () are characterized by simple scaling functions. In particular, the
fluctuations exhibit a cusp-like singularity at . Inside the spin-glass
region the average domain-wall energy converges to a finite nonzero value as
the sample size becomes infinite, holding fixed. Here, large finite-size
effects are visible, which can be explained for all by a single exponent
, provided higher-order corrections to scaling are included.
Finally, we confirm the validity of aspect-ratio scaling for : the
distribution of the domain-wall energies converges to a Gaussian for ,
although the domain walls of neighboring subsystems of size are
not independent.Comment: 11 pages with 15 figures, extensively revise
Reduction of Two-Dimensional Dilute Ising Spin Glasses
The recently proposed reduction method is applied to the Edwards-Anderson
model on bond-diluted square lattices. This allows, in combination with a
graph-theoretical matching algorithm, to calculate numerically exact ground
states of large systems. Low-temperature domain-wall excitations are studied to
determine the stiffness exponent y_2. A value of y_2=-0.281(3) is found,
consistent with previous results obtained on undiluted lattices. This
comparison demonstrates the validity of the reduction method for bond-diluted
spin systems and provides strong support for similar studies proclaiming
accurate results for stiffness exponents in dimensions d=3,...,7.Comment: 7 pages, RevTex4, 6 ps-figures included, for related information, see
http://www.physics.emory.edu/faculty/boettcher
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