upstage/dp-bench huggingface dataset:
content: text: At Home in Exile

content: text: Else had told us how phosphorenscence burning on human skin could not
be out, and how a seventeen-year-old soldier, weak from starvation,
put
had been fed at a stranger mother's breast in the bunker before he returned
to fight Russian soldiers in the final Breslau street battles. She had told us
how a fat man had wedged himself into the shelter's entrance, and had
been mown down by the hysterical mob. She had told us how she herself
had carried her sick mother across a burning rooftop.

content: text: Beneath the reconstructed Novi Targ square, John identified shelters in
two places, downstairs bolted against public entry. Plain and ugly high-
rise public housing of cheap materials now stood around the bare square,
where once interesting seventeenth-century merchant houses had stood
amid a lively marketplace. People had lived in apartments even before
the Communist-style transformations. Before their destruction, the old
buildings of Breslau were of stately proportions, made of good material
by experienced artisans who valued their talents and who took pride in
a town with depth to its history.

content: text: Novi Targ now looks much sadder and more neglected than glossy
my
photos show. Breslau's lively markets that were once a feature of the city,
as shown in my photographs of 1905, were relocated by the council in the
second half of the twentieth century to a large new market hall. This was
allegedly because of the congestion caused in the city's central squares by
traders with their cars, animals and stalls.

content: text: I was nevertheless deeply moved. This ugly restoration was on ground
where my grandmother and her children had walked so many times.
Grandmother Emma and beloved aunt Else had lived there for fifteen
my
years before 1945. My mother had corresponded with them from far away.

content: text: Had we stayed longer, we would have enjoyed other moments of pleasure
in a city that remains drab, and in which not even the theatre has been
restored. The original buildings, and what they stood for, were German.
The culture ofSilesia before 1945 has not yet been generally acknowledged.
It is also of Polish history. I am sure this will change.
part
content: text: Probability, Combinatorics and Control

content: text: ■ single-frequence ■ multi-frequence
0,3
0.25
damage
0,2
0.15
of
Level
0,1
0.05
0
1 2 3 4 5 6
Number of impellers

content: text: Figure 7.
Estimated cumulative damage for impeller blades.

content: text: ■ single-frequency ■ multi-frequency
8
7
6
years
5
Resource,
4
3
2
1
0
1 2 3 4 5 6
Number of impellers

content: text: Figure 8.
Estimated residual life of impeller blades by the criterion of cracking.

content: text: ■ single-frequence ■ multi-frequence
12
10
years
8
Resource,
6
4
2
0
1 2 3 4 5 6
Number of impellers

content: text: Figure 9.
Estimated residual life of impeller blades at the stage of crack development.
content: text: Probability, Combinatorics and Control

content: text: \lim\frac{P_{LL}}{P_{LH}+P_{HL}}\quad\text{and}\quad\lim\frac{P_{LL}+P_{HH}}{P_{LH}+P_{HL}}

content: text: (13)

content: text: equal zero when certain parameters tend to infinity in some well-defined way.
However, it is worthwhile at this stage to note their implications for cosmology.

content: text: The strong broken symmetry in Definition 5 actually means that a monotonic
behavior of the entropy is far more probable than a non-monotonic one. In the case
of a weak broken symmetry, this is not necessarily so; it could very well be that the
most probable scenario would be high entropy at both ends. Thus, this is definitely a
weaker statement, but it can nevertheless be argued that it can be used to explain
the time asymmetry that we observe, referring to a kind of anthropic principle: it is
an obvious observational fact that we live in a universe with low entropy at at least
one end. If the statement in Definition 4 is fulfilled, then clearly among such
scenarios, the monotonic ones (LH and HL) are the by far most probable ones.
Thus, since universes with high entropy at both ends would seem to be quite
uninhabitable, one can argue that given the existence of an observer, then with
almost certainty he must live in a universe with monotonic entropy.

content: text: Summing up, both limits above can be used to argue in favor of time asymmetry.
Nevertheless, at least to the mind of the author, the strong broken symmetry is the
preferable one. This alternative will be further studied in Section 9.

content: text: 8. Numerical computations in the combinatorial multiverse

content: text: With the setup in Sections 6 and 7, we can now use Mathematica or MATLAB to
generate instances of the combinatorial multiverse for small values of m and W and
then compute the corresponding probability weights PLL, PLH, PHL and PHH. It is
important to note that the matrices here can be treated as sparse, rather than as full
matrices, which make the computations considerably faster.

content: text: In particular, in the case m = 2 in Section 6 and with a randomly generated
dynamics which is manifested by an adjacency matrix A, we can compute the
power A4 and read of the first row, which contains all the information we need
about the paths from the state at t = -2 with S = 0. So what do we find?

content: text: In Figure 3, I have plotted the ratio NLL/(NLH + NHL) for the cases m = 2 (light
gray) and m = 3 (dark gray) for values of W ranging from 3 to 30. What is actually
displayed are the mean values of 1000 randomly generated matrices as above for
each value of W. Although the picture clearly supports the claim that

content: text: 0.10
0.08
0.06
0.04
0.02
0.00
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

content: text: Figure 3·
The ratio NLL/(NLH + NHL) as a function of W for the cases m = 2 (light gray) and m = 3 (dark gray) [4].
content: text: Prologue

content: text: Programming and Understanding

content: text: One way to become aware of the precision required to unam-
biguously communicate a mathematical idea is to program it for
a computer. Rather than using canned programs purely as an
aid to visualization or numerical computation, we use computer
programming in a functional style to encourage clear thinking.
Programming forces us to be precise and unambiguous, without
forcing us to be excessively rigorous. The computer does not toler-
ate vague descriptions or incomplete constructions. Thus the act
of programming makes us keenly aware of our errors of reasoning
or unsupported conclusions.1

content: text: Although this book is about differential geometry, we can show
how thinking about programming can help in understanding in a
more elementary context. The traditional use of Leibniz's notation
and Newton's notation is convenient in simple situations, but in
more complicated situations it can be a serious handicap to clear
reasoning.

content: text: A mechanical system is described by a Lagrangian function of
the system state (time, coordinates, and velocities). A motion of
the system is described by a path that gives the coordinates for
each moment of time. A path is allowed if and only if it satisfies
the Lagrange equations. Traditionally, the Lagrange equations are
written

content: text: \frac{d}{dt}\frac{\partialL}{\partial\dot{q}}-\frac{\partialL}{\partialq}=0.

content: text: What could this expression possibly mean?

content: text: Let's try to write a program that implements Lagrange equa-
tions. What are Lagrange equations for? Our program must take
a proposed path and give a result that allows us to decide if the
path is allowed. This is already a problem; the equation shown
above does not have a slot for a path to be tested.

content: text: 1The idea of using computer programming to develop skills of clear thinking
was originally advocated by Seymour Papert. An extensive discussion of this
idea, applied to the education of young children, can be found in Papert [13].
content: text: Prologue

content: text: xvii

content: text: Functional Abstraction

content: text: But this corrected use of Leibniz notation is ugly. We had to
introduce extraneous symbols (q and q) in order to indicate the ar-
gument position specifying the partial derivative. Nothing would
change here if we replaced q and q by a and b.3 We can sim-
plify the notation by admitting that the partial derivatives of the
Lagrangian are themselves new functions, and by specifying the
particular partial derivative by the position of the argument that
is varied

content: text: \frac{d}{dl}\left(\left(\partial_2L\right)\left(t,w(t),\frac{d}{dl}w(t)\right)\right)-\left(\partial_1L\right)\left(t,w(t),\frac{d}{dl}w(t)\right)=0,

content: text: where aiL is the function which is the partial derivative of the
4
function L with respect to the ith argument.

content: text: Two different notions of derivative appear in this expression.
The functions �2L and �1L, constructed from the Lagrangian
L, have the same arguments as L. The derivative d/dt is an
expression derivative. It applies to an expression that involves
the variable t and it gives the rate of change of the value of the
expression as the value of the variable t is varied.

content: text: These are both useful interpretations of the idea of a derivative.
But functions give us more power. There are many equivalent
ways to write expressions that compute the same value. For
example 1/(1/r1 + 1/r2) = (r1r2)/(r1 + r2). These expressions
compute the same function of the two variables r1 and r2. The
first expression fails if r1 = 0 but the second one gives the right
value of the function. If we abstract the function, say as II(r1, r2),
we can ignore the details of how it is computed. The ideas become
clearer because they do not depend on the detailed shape of the
expressions.

content: text: 3 That the symbols q and q can be replaced by other arbitrarily chosen non-
conflicting symbols without changing the meaning of the expression tells us
that the partial derivative symbol is a logical quantifier, like forall and exists
(∀ and ∃).
4The argument positions of the Lagrangian are indicated by indices starting
with zero for the time argument.
content: text: xviii

content: text: Prologue

content: text: So let's get rid of the expression derivative d/dt and replace it
with an appropriate functional derivative. If f is a function then
we will write Df as the new function that is the derivative of f:5

content: text: (Df)(t)=\left.\frac{d}{dx}f(x)\right|_{x=t}.

content: text: To do this for the Lagrange equation we need to construct a
function to take the derivative of.

content: text: Given a configuration-space path w, there is a standard way
to make the state-space path. We can abstract this method as a
mathematical function �:

content: text: \Gamma[w](t)=\left(t,w(t),\frac{d}{dl}w(t)\right).

content: text: Using � we can write:

content: text: \frac{d}{dt}\left(\left(\partial_2L\right)(\Gamma[w](t))\right)-\left(\partial_1L\right)(\Gamma[w(t))=0.

content: text: If we now define composition of functions (f ○ g)(x) = f(g(x)),
we can express the Lagrange equations entirely in terms of func-
tions:

content: text: D\left(\left(\partial_2L\right)\circ(\Gamma[w])\right)-\left(\partial_1L\right)\circ(\Gamma[w])=0.

content: text: The functions �1L and �2L are partial derivatives of the func-
tion L. Composition with �[w] evaluates these partials with coor-
dinates and velocites appropriate for the path w, making functions
of time. Applying D takes the time derivative. The Lagrange
equation states that the difference of the resulting functions of
time must be zero. This statement of the Lagrange equation is
complete, unambiguous, and functional. It is not encumbered
with the particular choices made in expressing the Lagrangian.
For example, it doesn't matter if the time is named t or �, and it
has an explicit place for the path to be tested.

content: text: This expression is equivalent to a computer program:6

content: text: 5An explanation of functional derivatives is in Appendix B, page 202.
6The programs in this book are written in Scheme, a dialect of Lisp. The
details of the language are not germane to the points being made. What is
important is that it is mechanically interpretable, and thus unambiguous. In
this book we require that the mathematical expressions be explicit enough
content: text: 4
Basis Fields

content: text: A vector field may be written as a linear combination of basis
vector fields. If n is the dimension, then any set of n linearly
independent vector fields may be used as a basis. The coordinate
basis X is an example of a basis.1 We will see later that not every
basis is a coordinate basis: in order to be a coordinate basis,
there must be a coordinate system such that each basis element is
the directional derivative operator in a corresponding coordinate
direction.

content: text: Let e be a tuple of basis vector fields, such as the coordinate
basis X. The general vector field v applied to an arbitrary manifold
function f can be expressed as a linear combination

content: text: \mathrm{v}(\mathrm{f})(\mathrm{m})=\mathrm{e}(\mathrm{f})(\mathrm{m})\mathrm{b}(\mathrm{m})=\sum_i\mathrm{e}_i(\mathrm{f})(\mathrm{m})\mathrm{b}^i(\mathrm{~m})\text{,}

content: text: (4.1)

content: text: where b is a tuple-valued coefficient function on the manifold.
When expressed in a coordinate basis, the coefficients that specify
the direction of the vector are naturally expressed as functions
bi of the coordinates of the manifold point. Here, the coefficient
function b is more naturally expressed as a tuple-valued function
on the manifold. If b is the coefficient function expressed as a
function of coordinates, then b = b ○ X is the coefficient function
as a function on the manifold.

content: text: The coordinate-basis forms have a simple definition in terms of
the coordinate-basis vectors and the coordinates (equation 3.40).
With this choice, the dual property, equation (3.41), holds without
further fuss. More generally, we can define a basis of one-forms e
that is dual to e in that the property

content: text: \tilde{\mathbf{e}}^i\left(\mathbf{e}_j\right)(\mathrm{m})=\delta_j^i

content: text: (4.2)

content: text: is satisfied, analogous to property (3.41). Figure 4.1 illustrates
the duality of basis fields.

content: text: 1We cannot say if the basis vectors are orthogonal or normalized until we
introduce a metric.
content: text: 2. General Profile of MSMEs

content: text: In July 2020, the survey established a general profile
of the MSMEs interviewed. The respondents updated
the interviewers on the status of their business in each
subsequent phase. Respondents whose business
had permanently closed were only asked the reasons
for closing (Section 2.4) and about government
assistance programs (Section 7). The demographics
of respondents and business characteristics (i.e., the
proportions) remained roughly the same across all
three survey phases.

content: text: Business characteristics. Business size was
determined by the number of staff at the time of
interview. Following Government Decree number 25/
GOV, firms with five or less staff are microenterprises,
those with six - 50 staff are small, and those with 51
- 99 staff are medium.

content: text: Micro and small enterprises made up most of
the respondents. Approximately 58% were
microenterprises, 40% were small, and only two

content: text: Figure 2.1: Surveyed MSMEs by size across sectors (%)

content: text: 2 1 4 1
100
37
80 40
40
50
60
40
62
58 56
49
20
0
All MSMEs Tourism Handicraft/Textile Agriculture
■ Micro ■ Small ■ Medium

content: text: percent were medium. The tourism MSME sample
included a higher percentage of microenterprises than
the othertwo sectors. All of the tourism and handicraft/
textile MSMEs interviewed were registered, orformal,
constituting approximately 71 % of the sample. The
remainder (agriculture MSMEs) were informal, as they
were individual farmers.

content: text: The geographic focus of sampling sought to emulate
the concentration of businesses nationwide.
Interviewed MSMEs in the tourism and handicraft/
textile sectors were mainly based in Vientiane Capital,
Luang Prabang, and Champasack provinces. For the
agriculture sector, MSMEs were based in 12 provinces
and the capital. Annex 1 provides the locations of
respondents who participated in all three phases.

content: text: The tourism sub-sectors interviewed included
lodging, restaurants and bars, and tour operators.
Most handicraft/textile respondents were involved
in production, with the remaining in sales. The

content: text: main products are silk and cotton products such as
bags, clothes, and scarves, bamboo wicker, pottery,
carvings, and mulberry paper products. MSMEs
interviewed in the agriculture sector focused on the
cultivation and trade of cash crops such as vegetables,
cassava, banana, sugar cane, tea and coffee, livestock
or fish, and rice.

content: text: Demographics of respondents. The overall gender
ratio of interviewees was slightly skewed towards
men (52%). Within the handicraft/textile sector,
80% were women, while the agriculture sector
was dominated by male representatives (74%). The
tourism sector respondents were 51% men. Most
of the interviewees were MSME owners (80%),
followed by managers (17%), while the other three
percent comprised positions such as accountant,
assistant, and deputy manager. More than half (58%)
of interviewees were 36 to 55 years old; the youngest
respondent was 23 and the eldest was 83.
content: text: 3. Impact on Business Operations

content: text: This section investigates the impact of public health
measures on business operations. MSMEs were
asked about their expectations for recovery and the
main effects of COVID-19 on their businesses.

content: text: 3.1. Status of Business Operations

content: text: As shown in Figure 3.1.1, the number of MSMEs
"working as usual" gradually increased over the

content: text: course of the research period. The impacts of the
lockdown from March 30 to May 4, 2020, were starkly
felt, with only 30% of the MSMEs "working as usual,"
while over half (58%) were temporarily completely
closed.

content: text: In the agriculture sector, a large majority of MSMEs
(93% in July 2020, 98% in October 2020, and 99%
in January 2021) were operating normally, though

content: text: Figure 3. 1. 1: Status of operations during each survey phase (%)

content: text: 2 2 1
100 1
6 2
5
7 13
13
21
80
60 58
85
40 83
71
20
30
0
Lockdown Period July 2020 October 2020 January 2021
Business premises closed to customers, but some business operations continue
Business premises still open, but reduced operations
Temporarily closed
Working as usual

content: text: during the first lockdown period, just over three
quarters (77%) were working as usual. In contrast,
63% of firms from the tourism sector and 62%
from the handicraft/textile sector were working as
usual as of July 2020, rising to 80% of tourism and
82% of handicraft/textile firms as of January 2021.
During the lockdown period, tourism and handicraft/
textile MSMEs were the hardest hit with just 12%
and 15% respectively working as usual. As shown
in Table 3.1.1., a majority of tourism and handicraft/
textile MSMEs were temporarily closed during the

content: text: lockdown period. In the handicraft/textile sector, 30%
of MSMEs were temporarily closed as of July 2020,
reducing to 12% in January 2021. Similarly, in tourism,
27% of businesses were temporarily closed as of July
2020 and that reduced to 18% in January 2021. Figure
3.1.1 and Table 3.1.1 do not reflect those MSMEs who
were permanently closed; this was four in July 2020,
22 in October 2020, and 24 in January 2021. Of these
50 businesses who permanently closed during the
research period, 30 were in the tourism sector, 18 in
handicraft/textile, and two in agriculture.
content: text: Figure 6.1.1: Will they fire more staff in the next 2 months - across survey phases (%)

content: text: 100
18
26
1
80
45
1
60
5
40 81 73
51
20
0
J uly 2020 October 2020 J anuary 2021
■ Will not terminate employment ■ Will terminate employment ■ Don't know

content: text: Figure 6.1.2: Will they fire more staff in the next 2 months - across sectors and survey phases (%)

content: text: 100
6 9
16
26
32 2
80
45
2 59
59
62
8
60
91
94
82
40
1
71
59
55
41 41
20 37
0
J ul 2020 Oct 2020 J an 2021 J ul 2020 Oct 2020 J an 2021 J ul 2020 Oct 2020 J an 2021
Tourism Handicraft/Textile Agriculture
■ Will not terminate employment ■ Will terminate employment ■ Don't know

content: text: 6.2. Expectations for Re-Hiring Employees

content: text: In July 2020, 81% of the MSMEs that had laid off
employees expected to re-hire all of them when the
situation improved. This number reduced to 23% in
October 2020 and further to just 7% in January 2021.5
In July 2020, all MSMEs had plans to re-hire at least
some of their staff. But in October 2020, 17% said

content: text: they had no plans to re-hire and another 36% said
they didn't know whether they would re-hire or not. In
January 2021, 20% said they had no plans to re-hire
and another 27% said they did not know. This question
was only posed to those who had let staff go since the
last survey round, and in October 2020 and January
2021, the base numbers reduced as fewer MSMEs
reported letting staff go. In July 2020, 195 MSMEs

content: text: 5. The question on re-hiring was asked to those who had laid-off employees since the last survey. In the latter two survey rounds,
respondents were asked about plans to re-hire staff whom they had let go since the previous interview, whereas in July 2020, they
were asked about plans to re-hire staff they had let go since their business was first affected by the pandemic.
content: text: Figure 9.4.1: Challenges in importing amongst tourism MSMEs who import - all survey phases (%)

content: text: 100
22
32 37
80
20
60
17
30
40
57
46
20 38
0
July 2020 October 2020 January 2021
■ Big Challenge ■ Small Challenge ■ No Challenge

content: text: There were very few tourism MSMEs that exported
in each survey round. The base is too small for any
conclusive analysis.

content: text: 9.5. Adapting to the New Normal: Changing
Business Models

content: text: In all survey phases, several MSMEs in the tourism
sector reported changing their business models. In
July 2020, 167 tourism MSMEs mentioned that they
changed their business model, in October 2020, 223
mentioned the same, and in January 2021, it was 183
MSMEs. Some changed models in more ways than
one. The main ways across all phases that MSMEs
made changes were:

content: text: · Adapting to social distancing;

content: text: · Devising new ways to reach customers through
online markets or social media;

content: text: · Moving into new products and services in high
demand during COVID-19;

content: text: · Reducing employee salaries.

content: text: Compared to previous survey round results, in
January 2021, tourism MSMEs had increasingly
shifted towards adapting to social distancing to
operate (57%).6 Starting online marketing remained a
popular choice, as nearly a quarter (24%) mentioned
it in January 2021, compared to 28% in July 2020 and
31 % in October 2020. Reducing employee salaries as
an approach reduced considerably in January 2021 at
8% of responses compared to 21 % in July 2020 and
24% in October 2020.

content: text: 6. Compared to 38% in July 2020 and 22% in October 2020.