3,396,539 research outputs found
Theory of Change
Horizon 2045 (H2045) is a 25-year initiative to end the nuclear weapons century.
We urgently need to manage the intertwined existential risks of the Anthropocene—the geological era that began with the 1945 Trinity Test and is characterized by humankind’s newfound capacity to destroy itself along with all life on the planet.
Recent research has shown that concerns about existential threats have become palpable, as has the desire to solve human-made problems and move to a brighter future. This offers an important opportunity: By considering nuclear weapons in the context of other dangers, we can dismantle conventional wisdom that nuclear weapons are tools for maintaining global stability, drawing new energy to the effort to rid ourselves of them.
What makes H2045 unique is that we bring a new theory of change. Rather than centering solely on nuclear weapons, our theory of change creates common ground for organizations and thought leaders who share our vision: Humanity can, and will, move beyond the existential challenges we now face. By shifting our sole focus from nuclear challenges to a broader conception of global security, we increase the surface area for collaboration and shared learning. In so doing, we lay the groundwork for a much larger-scale effort.
This document is an invitation to think with us. It is the product of a collaborative effort. It is a snapshot of a work in process. It raises more questions than it answers. It is intended to shake the current paradigm. It uses speculative techniques to bring alternate futures to life. It may cause discomfort. It may cause inspiration.
We think this kind of work is important in shaping debates, changing narratives, and provoking change. We invite you to use this document as a jumping off point for thinking big and long term. It does not need to be read all at once. You may skip to the section that seems most intriguing and start there. What questions does it raise for you? What questions remain to be asked and answered? What answers might you have?
There is a great deal that must be done. In our next phase we will be working to translate these insights into pragmatic solutions. Inspiration and vision light the way for that journey. H2045 will expand to include others in the development of a vision that inspires change.https://digitalcommons.risd.edu/cfc_projectsprograms_globalsecurity_horizon2045/1001/thumbnail.jp
Algorithms and Bounds for Very Strong Rainbow Coloring
A well-studied coloring problem is to assign colors to the edges of a graph
so that, for every pair of vertices, all edges of at least one shortest
path between them receive different colors. The minimum number of colors
necessary in such a coloring is the strong rainbow connection number
(\src(G)) of the graph. When proving upper bounds on \src(G), it is natural
to prove that a coloring exists where, for \emph{every} shortest path between
every pair of vertices in the graph, all edges of the path receive different
colors. Therefore, we introduce and formally define this more restricted edge
coloring number, which we call \emph{very strong rainbow connection number}
(\vsrc(G)).
In this paper, we give upper bounds on \vsrc(G) for several graph classes,
some of which are tight. These immediately imply new upper bounds on \src(G)
for these classes, showing that the study of \vsrc(G) enables meaningful
progress on bounding \src(G). Then we study the complexity of the problem to
compute \vsrc(G), particularly for graphs of bounded treewidth, and show this
is an interesting problem in its own right. We prove that \vsrc(G) can be
computed in polynomial time on cactus graphs; in contrast, this question is
still open for \src(G). We also observe that deciding whether \vsrc(G) = k
is fixed-parameter tractable in and the treewidth of . Finally, on
general graphs, we prove that there is no polynomial-time algorithm to decide
whether \vsrc(G) \leq 3 nor to approximate \vsrc(G) within a factor
, unless PNP
Restricted Complexity, General Complexity
Why has the problematic of complexity appeared so late? And why would it be justified
After the A-Bomb
RISD’s Center for Complexity launches Horizon 2045, a 25-year project aimed at eliminating the threat of nuclear war.https://digitalcommons.risd.edu/cfc_projectsprograms_globalsecurity_horizon2045/1000/thumbnail.jp
Time complexity and gate complexity
We formulate and investigate the simplest version of time-optimal quantum
computation theory (t-QCT), where the computation time is defined by the
physical one and the Hamiltonian contains only one- and two-qubit interactions.
This version of t-QCT is also considered as optimality by sub-Riemannian
geodesic length. The work has two aims: one is to develop a t-QCT itself based
on physically natural concept of time, and the other is to pursue the
possibility of using t-QCT as a tool to estimate the complexity in conventional
gate-optimal quantum computation theory (g-QCT). In particular, we investigate
to what extent is true the statement: time complexity is polynomial in the
number of qubits if and only if so is gate complexity. In the analysis, we
relate t-QCT and optimal control theory (OCT) through fidelity-optimal
computation theory (f-QCT); f-QCT is equivalent to t-QCT in the limit of unit
optimal fidelity, while it is formally similar to OCT. We then develop an
efficient numerical scheme for f-QCT by modifying Krotov's method in OCT, which
has monotonic convergence property. We implemented the scheme and obtained
solutions of f-QCT and of t-QCT for the quantum Fourier transform and a unitary
operator that does not have an apparent symmetry. The former has a polynomial
gate complexity and the latter is expected to have exponential one because a
series of generic unitary operators has a exponential gate complexity. The time
complexity for the former is found to be linear in the number of qubits, which
is understood naturally by the existence of an upper bound. The time complexity
for the latter is exponential. Thus the both targets are examples satisfyng the
statement above. The typical characteristics of the optimal Hamiltonians are
symmetry under time-reversal and constancy of one-qubit operation, which are
mathematically shown to hold in fairly general situations.Comment: 11 pages, 6 figure
Descriptive Complexity for Counting Complexity Classes
Descriptive Complexity has been very successful in characterizing complexity
classes of decision problems in terms of the properties definable in some
logics. However, descriptive complexity for counting complexity classes, such
as FP and #P, has not been systematically studied, and it is not as developed
as its decision counterpart. In this paper, we propose a framework based on
Weighted Logics to address this issue. Specifically, by focusing on the natural
numbers we obtain a logic called Quantitative Second Order Logics (QSO), and
show how some of its fragments can be used to capture fundamental counting
complexity classes such as FP, #P and FPSPACE, among others. We also use QSO to
define a hierarchy inside #P, identifying counting complexity classes with good
closure and approximation properties, and which admit natural complete
problems. Finally, we add recursion to QSO, and show how this extension
naturally captures lower counting complexity classes such as #L
- …