4,809 research outputs found
A non Supersymmetric SO(10) Grand Unified Model for All the Physics below
We present a renormalizable non supersymmetric Grand Unified SO(10) model
which, at the price of a large fine tuning, is compatible with all compelling
phenomenological requirements below the unification scale and thus realizes a
minimal extension of the SM, unified in SO(10) and describing all known physics
below . These requirements include coupling unification at a large
enough scale to be compatible with the bounds on proton decay; a Yukawa sector
in agreement with all the data on quark and lepton masses and mixings and with
leptogenesis as the origin of the baryon asymmetry of the Universe; an axion
arising from the Higgs sector of the model, suitable to solve the strong CP
problem and to account for the observed amount of Dark Matter. The above
constraints imposed by the data are very stringent and single out a particular
breaking chain with the Pati-Salam group at an intermediate scale
GeV.Comment: references added, minor changes in the text, version to appear in
JHE
Evaluating the impact of innovation incentives: evidence from an unexpected shortage of funds
To evaluate the effect of an R&D subsidy one needs to know what the subsidized firms would have done without the incentive. This paper studies an Italian programme of subsidies for the applied development of innovations, exploiting a discontinuity in programme financing due to an unexpected shortage of public money. To identify the effect of the programme, the study implements a regression discontinuity design and compares firms that applied for funding before and after the shortage occurred. The results indicate that the programme was not effective in stimulating innovative investment.R&D, public policy, evaluation
On Sub-Propositional Fragments of Modal Logic
In this paper, we consider the well-known modal logics ,
, , and , and we study some of their
sub-propositional fragments, namely the classical Horn fragment, the Krom
fragment, the so-called core fragment, defined as the intersection of the Horn
and the Krom fragments, plus their sub-fragments obtained by limiting the use
of boxes and diamonds in clauses. We focus, first, on the relative expressive
power of such languages: we introduce a suitable measure of expressive power,
and we obtain a complex hierarchy that encompasses all fragments of the
considered logics. Then, after observing the low expressive power, in
particular, of the Horn fragments without diamonds, we study the computational
complexity of their satisfiability problem, proving that, in general, it
becomes polynomial
Long-range Ising and Kitaev Models: Phases, Correlations and Edge Modes
We analyze the quantum phases, correlation functions and edge modes for a
class of spin-1/2 and fermionic models related to the 1D Ising chain in the
presence of a transverse field. These models are the Ising chain with
anti-ferromagnetic long-range interactions that decay with distance as
, as well as a related class of fermionic Hamiltonians that
generalise the Kitaev chain, where both the hopping and pairing terms are
long-range and their relative strength can be varied. For these models, we
provide the phase diagram for all exponents , based on an analysis of
the entanglement entropy, the decay of correlation functions, and the edge
modes in the case of open chains. We demonstrate that violations of the area
law can occur for , while connected correlation functions can
decay with a hybrid exponential and power-law behaviour, with a power that is
-dependent. Interestingly, for the fermionic models we provide an exact
analytical derivation for the decay of the correlation functions at every
. Along the critical lines, for all models breaking of conformal
symmetry is argued at low enough . For the fermionic models we show
that the edge modes, massless for , can acquire a mass for
. The mass of these modes can be tuned by varying the relative
strength of the kinetic and pairing terms in the Hamiltonian. Interestingly,
for the Ising chain a similar edge localization appears for the first and
second excited states on the paramagnetic side of the phase diagram, where edge
modes are not expected. We argue that, at least for the fermionic chains, these
massive states correspond to the appearance of new phases, notably approached
via quantum phase transitions without mass gap closure. Finally, we discuss the
possibility to detect some of these effects in experiments with cold trapped
ions.Comment: 15 pages, 8 figure
Multiple-Edge-Fault-Tolerant Approximate Shortest-Path Trees
Let be an -node and -edge positively real-weighted undirected
graph. For any given integer , we study the problem of designing a
sparse \emph{f-edge-fault-tolerant} (-EFT) {\em -approximate
single-source shortest-path tree} (-ASPT), namely a subgraph of
having as few edges as possible and which, following the failure of a set
of at most edges in , contains paths from a fixed source that are
stretched at most by a factor of . To this respect, we provide an
algorithm that efficiently computes an -EFT -ASPT of size . Our structure improves on a previous related construction designed for
\emph{unweighted} graphs, having the same size but guaranteeing a larger
stretch factor of , plus an additive term of .
Then, we show how to convert our structure into an efficient -EFT
\emph{single-source distance oracle} (SSDO), that can be built in
time, has size , and is able to report,
after the failure of the edge set , in time a
-approximate distance from the source to any node, and a
corresponding approximate path in the same amount of time plus the path's size.
Such an oracle is obtained by handling another fundamental problem, namely that
of updating a \emph{minimum spanning forest} (MSF) of after that a
\emph{batch} of simultaneous edge modifications (i.e., edge insertions,
deletions and weight changes) is performed. For this problem, we build in time a \emph{sensitivity} oracle of size , that
reports in time the (at most ) edges either exiting from
or entering into the MSF. [...]Comment: 16 pages, 4 figure
The Max-Distance Network Creation Game on General Host Graphs
In this paper we study a generalization of the classic \emph{network creation
game} in the scenario in which the players sit on a given arbitrary
\emph{host graph}, which constrains the set of edges a player can activate at a
cost of each. This finds its motivations in the physical
limitations one can have in constructing links in practice, and it has been
studied in the past only when the routing cost component of a player is given
by the sum of distances to all the other nodes. Here, we focus on another
popular routing cost, namely that which takes into account for each player its
\emph{maximum} distance to any other player. For this version of the game, we
first analyze some of its computational and dynamic aspects, and then we
address the problem of understanding the structure of associated pure Nash
equilibria. In this respect, we show that the corresponding price of anarchy
(PoA) is fairly bad, even for several basic classes of host graphs. More
precisely, we first exhibit a lower bound of
for any . Notice that this implies a counter-intuitive lower
bound of for very small values of (i.e., edges can
be activated almost for free). Then, we show that when the host graph is
restricted to be either -regular (for any constant ), or a
2-dimensional grid, the PoA is still , which is proven to be tight for
. On the positive side, if , we show
the PoA is . Finally, in the case in which the host graph is very sparse
(i.e., , with ), we prove that the PoA is , for any
.Comment: 17 pages, 4 figure
Specializations and Generalizations of the Stackelberg Minimum Spanning Tree Game
Let be given a graph whose edge set is partitioned into a set
of \emph{red} edges and a set of \emph{blue} edges, and assume that red
edges are weighted and form a spanning tree of . Then, the \emph{Stackelberg
Minimum Spanning Tree} (\stack) problem is that of pricing (i.e., weighting)
the blue edges in such a way that the total weight of the blue edges selected
in a minimum spanning tree of the resulting graph is maximized. \stack \ is
known to be \apx-hard already when the number of distinct red weights is 2. In
this paper we analyze some meaningful specializations and generalizations of
\stack, which shed some more light on the computational complexity of the
problem. More precisely, we first show that if is restricted to be
\emph{complete}, then the following holds: (i) if there are only 2 distinct red
weights, then the problem can be solved optimally (this contrasts with the
corresponding \apx-hardness of the general problem); (ii) otherwise, the
problem can be approximated within , for any .
Afterwards, we define a natural extension of \stack, namely that in which blue
edges have a non-negative \emph{activation cost} associated, and it is given a
global \emph{activation budget} that must not be exceeded when pricing blue
edges. Here, after showing that the very same approximation ratio as that of
the original problem can be achieved, we prove that if the spanning tree of red
edges can be rooted so as that any root-leaf path contains at most edges,
then the problem admits a -approximation algorithm, for any
.Comment: 22 pages, 7 figure
- âŠ