141 research outputs found
The secretary problem with a selection committee : do conformist committees hire better secretaries
This paper analyzes a variation of the secretary problem in which two selectors with different fields of interest each want to appoint one of the n candidates with as much expertise as possible in their field. Selectors simultaneously vote to accept or reject: Unanimous decisions are respected, and candidates with a split decision are hired with probability p. Each candidate arrives with expertise x and y in the two fields, uniformly and independently distributed on [0, 1] and observable to both selectors. If a candidate with expertise pair (x, y) is hired by unanimous decision, the payoffs to the selectors are simply x and y. However, to model the level of conformity in the firm, we deduct a positive “consensus cost” c from the utility of a selector who has rejected a candidate who is nevertheless hired. We show (Theorem 1) that each stage game has a unique equilibrium in which there are two thresholds, z v or x > z and y > v. We show that for sufficiently large p and c, decisions are unanimous, and that as the number n of candidates goes to infinity, the equilibrium value of the game goes to the golden mean. We show that as the consensus cost c increases from 0, this hurts the selectors (Theorem 4) but helps the firm (Theorem 6), whose utility from hiring candidate (x, y) is a weighted average of x and y. Thus a little conformity is good for the firm
Rendezvous of Heterogeneous Mobile Agents in Edge-weighted Networks
We introduce a variant of the deterministic rendezvous problem for a pair of
heterogeneous agents operating in an undirected graph, which differ in the time
they require to traverse particular edges of the graph. Each agent knows the
complete topology of the graph and the initial positions of both agents. The
agent also knows its own traversal times for all of the edges of the graph, but
is unaware of the corresponding traversal times for the other agent. The goal
of the agents is to meet on an edge or a node of the graph. In this scenario,
we study the time required by the agents to meet, compared to the meeting time
in the offline scenario in which the agents have complete knowledge
about each others speed characteristics. When no additional assumptions are
made, we show that rendezvous in our model can be achieved after time in a -node graph, and that such time is essentially in some cases
the best possible. However, we prove that the rendezvous time can be reduced to
when the agents are allowed to exchange bits of
information at the start of the rendezvous process. We then show that under
some natural assumption about the traversal times of edges, the hardness of the
heterogeneous rendezvous problem can be substantially decreased, both in terms
of time required for rendezvous without communication, and the communication
complexity of achieving rendezvous in time
Management of a Case of Colovesical Fistula with Fecaluria as First Sign
Introduction. Fecaluria and pneumaturia are the patognomonic signs of an abnormal communication between the bladder and the intestinal tract. Therefore, when a history of digestive signs, symptoms or digestive diseases is missing, this borderline pathology leads the patients in the care of urologists. From diagnosis to treatment the management of these cases can be difficult and challenging.
Materials and Methods. A 48 year old patient, without any significant medical history, presented to the emergency room for fecaluria, pneumaturia and an episode of haematuria. He had no prior digestive symptoms. The contrast enhanced abdominal and pelvic CT scan revealed a pelvic mass involving the sigmoid colon and the dome and the posterior wall of the bladder. The cystoscopy objectifies a tumor mass involving the right postero-lateral bladder wall, with extravasation of faeces. A biopsy was taken and the frozen section found mainly uncertain inflammatory type tissue. A colonoscopy couldn’t be done because of an impassable obstacle at 15 cm from the anus. Together with general surgeons we decided for en bloc resection of the tumor with partial cystectomy, right ureterocystoneostomy and rectosigmoid resection with mechanic end to end anastomosis.
Results. The postoperative period was uneventful. The histopathological examination revealed an abscessed sigmoid diverticulum with vesico-sigmoid fistula and perilesional inflammatory tissue. Two years after the surgery the patient is asymptomatic with a normal function of the right kidney and restored bladder capacity.
Conclusions. Being a borderline pathology, patients with fecaluria and pneumaturia and lack of digestive symptoms are referred and managed by the urologists. Despite extensive investigations, even when preoperative biopsies reveal inflammatory tissue the patients should be treated as oncologic cases. A close cooperation with general surgeons for en bloc multiorgan resection within oncologic safety margins is mandatory
Differential Calculi on Some Quantum Prehomogeneous Vector Spaces
This paper is devoted to study of differential calculi over quadratic
algebras, which arise in the theory of quantum bounded symmetric domains. We
prove that in the quantum case dimensions of the homogeneous components of the
graded vector spaces of k-forms are the same as in the classical case. This
result is well-known for quantum matrices.
The quadratic algebras, which we consider in the present paper, are
q-analogues of the polynomial algebras on prehomogeneous vector spaces of
commutative parabolic type. This enables us to prove that the de Rham complex
is isomorphic to the dual of a quantum analogue of the generalized
Bernstein-Gelfand-Gelfand resolution.Comment: LaTeX2e, 51 pages; changed conten
Rendezvous of Distance-aware Mobile Agents in Unknown Graphs
We study the problem of rendezvous of two mobile agents starting at distinct
locations in an unknown graph. The agents have distinct labels and walk in
synchronous steps. However the graph is unlabelled and the agents have no means
of marking the nodes of the graph and cannot communicate with or see each other
until they meet at a node. When the graph is very large we want the time to
rendezvous to be independent of the graph size and to depend only on the
initial distance between the agents and some local parameters such as the
degree of the vertices, and the size of the agent's label. It is well known
that even for simple graphs of degree , the rendezvous time can be
exponential in in the worst case. In this paper, we introduce a new
version of the rendezvous problem where the agents are equipped with a device
that measures its distance to the other agent after every step. We show that
these \emph{distance-aware} agents are able to rendezvous in any unknown graph,
in time polynomial in all the local parameters such the degree of the nodes,
the initial distance and the size of the smaller of the two agent labels . Our algorithm has a time complexity of
and we show an almost matching lower bound of
on the time complexity of any
rendezvous algorithm in our scenario. Further, this lower bound extends
existing lower bounds for the general rendezvous problem without distance
awareness
Gathering in Dynamic Rings
The gathering problem requires a set of mobile agents, arbitrarily positioned
at different nodes of a network to group within finite time at the same
location, not fixed in advanced.
The extensive existing literature on this problem shares the same fundamental
assumption: the topological structure does not change during the rendezvous or
the gathering; this is true also for those investigations that consider faulty
nodes. In other words, they only consider static graphs. In this paper we start
the investigation of gathering in dynamic graphs, that is networks where the
topology changes continuously and at unpredictable locations.
We study the feasibility of gathering mobile agents, identical and without
explicit communication capabilities, in a dynamic ring of anonymous nodes; the
class of dynamics we consider is the classic 1-interval-connectivity.
We focus on the impact that factors such as chirality (i.e., a common sense
of orientation) and cross detection (i.e., the ability to detect, when
traversing an edge, whether some agent is traversing it in the other
direction), have on the solvability of the problem. We provide a complete
characterization of the classes of initial configurations from which the
gathering problem is solvable in presence and in absence of cross detection and
of chirality. The feasibility results of the characterization are all
constructive: we provide distributed algorithms that allow the agents to
gather. In particular, the protocols for gathering with cross detection are
time optimal. We also show that cross detection is a powerful computational
element.
We prove that, without chirality, knowledge of the ring size is strictly more
powerful than knowledge of the number of agents; on the other hand, with
chirality, knowledge of n can be substituted by knowledge of k, yielding the
same classes of feasible initial configurations
Almost optimal asynchronous rendezvous in infinite multidimensional grids
Two anonymous mobile agents (robots) moving in an asynchronous manner have to meet in an infinite grid of dimension δ> 0, starting from two arbitrary positions at distance at most d. Since the problem is clearly infeasible in such general setting, we assume that the grid is embedded in a δ-dimensional Euclidean space and that each agent knows the Cartesian coordinates of its own initial position (but not the one of the other agent). We design an algorithm permitting the agents to meet after traversing a trajectory of length O(d δ polylog d). This bound for the case of 2d-grids subsumes the main result of [12]. The algorithm is almost optimal, since the Ω(d δ) lower bound is straightforward. Further, we apply our rendezvous method to the following network design problem. The ports of the δ-dimensional grid have to be set such that two anonymous agents starting at distance at most d from each other will always meet, moving in an asynchronous manner, after traversing a O(d δ polylog d) length trajectory. We can also apply our method to a version of the geometric rendezvous problem. Two anonymous agents move asynchronously in the δ-dimensional Euclidean space. The agents have the radii of visibility of r1 and r2, respectively. Each agent knows only its own initial position and its own radius of visibility. The agents meet when one agent is visible to the other one. We propose an algorithm designing the trajectory of each agent, so that they always meet after traveling a total distance of O( ( d)), where r = min(r1, r2) and for r ≥ 1. r)δpolylog ( d r
Twistors and Black Holes
Motivated by black hole physics in N=2, D=4 supergravity, we study the
geometry of quaternionic-Kahler manifolds M obtained by the c-map construction
from projective special Kahler manifolds M_s. Improving on earlier treatments,
we compute the Kahler potentials on the twistor space Z and Swann space S in
the complex coordinates adapted to the Heisenberg symmetries. The results bear
a simple relation to the Hesse potential \Sigma of the special Kahler manifold
M_s, and hence to the Bekenstein-Hawking entropy for BPS black holes. We
explicitly construct the ``covariant c-map'' and the ``twistor map'', which
relate real coordinates on M x CP^1 (resp. M x R^4/Z_2) to complex coordinates
on Z (resp. S). As applications, we solve for the general BPS geodesic motion
on M, and provide explicit integral formulae for the quaternionic Penrose
transform relating elements of H^1(Z,O(-k)) to massless fields on M annihilated
by first or second order differential operators. Finally, we compute the exact
radial wave function (in the supergravity approximation) for BPS black holes
with fixed electric and magnetic charges.Comment: 47 pages, v2: typos corrected, reference added, v3: minor change
From 2D conformal to 4D self-dual theories: quaternionic analyticity
It is shown that self-dual theories generalize to four dimensions both the
conformal and analytic aspects of two-dimensional conformal field theories. In
the harmonic space language there appear several ways to extend complex
analyticity (natural in two dimensions) to quaternionic analyticity (natural in
four dimensions). To be analytic, conformal transformations should be realized
on , which appears as the coset of the complexified conformal group
modulo its maximal parabolic subgroup. In this language one visualizes the
twistor correspondence of Penrose and Ward and consistently formulates the
analyticity of Fueter.Comment: 24 pages, LaTe
Large scale three-dimensional modelling for wave and tidal energy resource and environmental impact : methodologies for quantifying acceptable thresholds for sustainable exploitation
We describe a modelling project to estimate the potential effects of wave & tidal stream renewables on the marine environment. • Realistic generic devices to be used by those without access to the technical details available to developers are described. • Results show largely local sea bed effects at the level of the currently proposed renewables developments in our study area. • Large scale 3D modelling is critical to quantify the direct, indirect and cumulative effects of renewable energy extraction. • This is critical to comply with planning & environmental impact assessment regulations and achieve Good Environmental Status
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