2,653 research outputs found
Fast Compact Laser Shutter Using a Direct Current Motor and 3D Printing
We present a mechanical laser shutter design that utilizes a DC electric
motor to rotate a blade which blocks and unblocks a light beam. The blade and
the main body of the shutter are modeled with computer aided design (CAD) and
are produced by 3D printing. Rubber flaps are used to limit the blade's range
of motion, reducing vibrations and preventing undesirable blade oscillations.
At its nominal operating voltage, the shutter achieves a switching speed of
(1.22 0.02) m/s with 1 ms activation delay and 10 s jitter in its
timing performance. The shutter design is simple, easy to replicate, and highly
reliable, showing no failure or degradation in performance over more than
cycles.Comment: 4 pages, 6 figures; supplementary materials for shutter replication
added under "Ancillary files
A finite analog of the AGT relation I: finite W-algebras and quasimaps' spaces
Recently Alday, Gaiotto and Tachikawa proposed a conjecture relating
4-dimensional super-symmetric gauge theory for a gauge group G with certain
2-dimensional conformal field theory. This conjecture implies the existence of
certain structures on the (equivariant) intersection cohomology of the
Uhlenbeck partial compactification of the moduli space of framed G-bundles on
P^2. More precisely, it predicts the existence of an action of the
corresponding W-algebra on the above cohomology, satisfying certain properties.
We propose a "finite analog" of the (above corollary of the) AGT conjecture.
Namely, we replace the Uhlenbeck space with the space of based quasi-maps from
P^1 to any partial flag variety G/P of G and conjecture that its equivariant
intersection cohomology carries an action of the finite W-algebra U(g,e)
associated with the principal nilpotent element in the Lie algebra of the Levi
subgroup of P; this action is expected to satisfy some list of natural
properties. This conjecture generalizes the main result of arXiv:math/0401409
when P is the Borel subgroup. We prove our conjecture for G=GL(N), using the
works of Brundan and Kleshchev interpreting the algebra U(g,e) in terms of
certain shifted Yangians.Comment: minor change
Torus fibrations and localization of index II
We give a framework of localization for the index of a Dirac-type operator on
an open manifold. Suppose the open manifold has a compact subset whose
complement is covered by a family of finitely many open subsets, each of which
has a structure of the total space of a torus bundle. Under an acyclic
condition we define the index of the Dirac-type operator by using the
Witten-type deformation, and show that the index has several properties, such
as excision property and a product formula. In particular, we show that the
index is localized on the compact set.Comment: 47 pages, 2 figures. To appear in Communications in Mathematical
Physic
Termination of Triangular Integer Loops is Decidable
We consider the problem whether termination of affine integer loops is
decidable. Since Tiwari conjectured decidability in 2004, only special cases
have been solved. We complement this work by proving decidability for the case
that the update matrix is triangular.Comment: Full version (with proofs) of a paper published in the Proceedings of
the 31st International Conference on Computer Aided Verification (CAV '19),
New York, NY, USA, Lecture Notes in Computer Science, Springer-Verlag, 201
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Teamworking and Lean revisited: a reply to Carter et al
This paper is a reply to Carter et al.’s response to an earlier paper of ours in this journal on the subject of teamworking under Lean in the UK public services . Our reply covers the following issues which Carter et al. have raised: the literature we used to structure our findings; the way in which we used concepts such as autonomy and teamworking; our research methods and approach; how Carter et al.’s newly available data on teamworking might be interpreted; and how data drawn from an official employee attitude survey might best be understood. On the basis of this, we conclude that Carter et al.’s paper fails to meet its objectives. On some things, the authors are simply wrong; on others, they grossly misrepresent our position; on still others, their interpretations are, at best, highly questionable
Limits of Quantum Speed-Ups for Computational Geometry and Other Problems: Fine-Grained Complexity via Quantum Walks
Many computational problems are subject to a quantum speed-up: one might find that a problem having an Opn3q-time or Opn2q-time classic algorithm can be solved by a known Opn1.5q-time or Opnq-time quantum algorithm. The question naturally arises: how much quantum speed-up is possible? The area of fine-grained complexity allows us to prove optimal lower-bounds on the complexity of various computational problems, based on the conjectured hardness of certain natural, well-studied problems. This theory has recently been extended to the quantum setting, in two independent papers by Buhrman, Patro and Speelman [7], and by Aaronson, Chia, Lin, Wang, and Zhang [1]. In this paper, we further extend the theory of fine-grained complexity to the quantum setting. A fundamental conjecture in the classical setting states that the 3SUM problem cannot be solved by (classical) algorithms in time Opn2´εq, for any ε ą 0. We formulate an analogous conjecture, the Quantum-3SUM-Conjecture, which states that there exist no sublinear Opn1´εq-time quantum algorithms for the 3SUM problem. Based on the Quantum-3SUM-Conjecture, we show new lower-bounds on the time complexity of quantum algorithms for several computational problems. Most of our lower-bounds are optimal, in that they match known upper-bounds, and hence they imply tight limits on the quantum speedup that is possible for these problems. These results are proven by adapting to the quantum setting known classical fine-grained reductions from the 3SUM problem. This adaptation is not trivial, however, since the original classical reductions require pre-processing the input in various ways, e.g. by sorting it according to some order, and this pre-processing (provably) cannot be done in sublinear quantum time. We overcome this bottleneck by combining a quantum walk with a classical dynamic data-structure having a certain “history-independence” property. This type of construction has been used in the past to prove upper bounds, and here we use it for the first time as part of a reduction. This general proof strategy allows us to prove tight lower bounds on several computational-geometry problems, on Convolution-3SUM and on the 0-Edge-Weight-Triangle problem, conditional on the Quantum-3SUM-Conjecture. We believe this proof strategy will be useful in proving tight (conditional) lower-bounds, and limits on quantum speed-ups, for many other problems
Larger Corner-Free Sets from Combinatorial Degenerations
There is a large and important collection of Ramsey-type combinatorial
problems, closely related to central problems in complexity theory, that can be
formulated in terms of the asymptotic growth of the size of the maximum
independent sets in powers of a fixed small (directed or undirected)
hypergraph, also called the Shannon capacity. An important instance of this is
the corner problem studied in the context of multiparty communication
complexity in the Number On the Forehead (NOF) model. Versions of this problem
and the NOF connection have seen much interest (and progress) in recent works
of Linial, Pitassi and Shraibman (ITCS 2019) and Linial and Shraibman (CCC
2021).
We introduce and study a general algebraic method for lower bounding the
Shannon capacity of directed hypergraphs via combinatorial degenerations, a
combinatorial kind of "approximation" of subgraphs that originates from the
study of matrix multiplication in algebraic complexity theory (and which play
an important role there) but which we use in a novel way.
Using the combinatorial degeneration method, we make progress on the corner
problem by explicitly constructing a corner-free subset in
of size , which improves the previous lower bound
of Linial, Pitassi and Shraibman (ITCS 2019) and which gets us
closer to the best upper bound . Our new construction of
corner-free sets implies an improved NOF protocol for the Eval problem. In the
Eval problem over a group , three players need to determine whether their
inputs sum to zero. We find that the NOF communication
complexity of the Eval problem over is at most ,
which improves the previous upper bound .Comment: A short version of this paper will appear in the proceedings of ITCS
2022. This paper improves results that appeared in arxiv:2104.01130v
Spatial and temporal characterization of a Bessel beam produced using a conical mirror
We experimentally analyze a Bessel beam produced with a conical mirror,
paying particular attention to its superluminal and diffraction-free
properties. We spatially characterized the beam in the radial and on-axis
dimensions, and verified that the central peak does not spread over a
propagation distance of 73 cm. In addition, we measured the superluminal phase
and group velocities of the beam in free space. Both spatial and temporal
measurements show good agreement with the theoretical predictions.Comment: 5 pages, 6 figure
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